Having given some thought on the issue, I agree that NATO smashing its way throughout Kosovo and possibly into Serbia itself would not be any really more difficult than conquering Kuwait and Iraq.
As other have pointed out, Kosovo only has mountains at its borders. The main difficulty was adapting Albanian roads to heavy military traffic and that's something NATO engineer corps could do in a few weeks to months (and indeed they were busy doing it in the last phase of the war, just in case, if the air offensive had not worked). Invading Serbia itself is just a problem of concentrating the appropriate amount of forces in Hungary and Romania, which are in all likelihood eager to cooperate with NATO.
The main problem is political will and perceived need in the West. While if Milosevic had not given up as he did, NATO would have reluctantly gone for ground invasion, they had staked far too much credibility to give up, I think it is much more plausible and interesting if we have NATO planning and preparing for ground invasion from the start after a preliminary air offensive, just like Gulf War and Iraq War. The way to do it is to make the Milosevic regime look even more "nasty" and threatening to the region, in addition to being more bullheaded nationalist and refusing compromise to the bitter end. At differing degrees, this may result both into limited ground invasion of Kosovo (the Kuwait-like scenario) or in invasion of Serbia itself (the Iraq-like scenario).
Ways to do it:
* The Serbs stage their large-scale mass expulsion of Kosovo Albanians before NATO starts the bombing. The televised images of 1 million "European Palestinians" massing in Albanian and Macedonian refugee camps without any plausible Western provocation can easily persuade the Western public opinion, US Congress, and European Parliaments to give a more explicit sanction to intervention and makes a credible reason why ground invasion looks necessary from the start to "bring the refugees back, the Serbs out, the peacekeepers in". It may or may not shame Russia and China into giving an UN blessing for NATO intervention and it may or may not enlarge the planned offensive to Serbia itself for a regime change. Most likely it does not but Western public opinion would give its governments a clear go-ahead for full-scale military intervention and Russia is a bit more motivated to look the other way. Ground offensive in Kosovo is planned from the start if Milosevic does not gives it up, invasion of Serbia may or may not be deemed necessary, most likely it does not.
* Serbia invades Albania and/or Macedonia in "hot pursuit" of the KLA before NATO starts its build-up. It makes Milosevic a clearer case for threat to international security of the region, both in the eyes of Western public and of Russia and China, if anything can convince the latter not to veto UN sanction to NATO intervention, this would be. Ground offensive in Kosovo is planned from the start if Milosevic does not gives it and occupied areas up, invasion of Serbia may or may not be deemed necessary, most likely it does not.
* Serbia previously gets an even dirtier record in Bosnia than OTL, with more large-scale massacres of Muslim Bosnians and/or murder of captured UN peacekeepers. It gets bullied into giving up Bosnia with NATO air offensive all the same, but it remains more of a pariah state. When it repeats its own ethnic cleansing shenanigans in Kosovo, NATO escalates to full-scale military intervention with the blessing of Western public opinion. Ground offensive in Kosovo is planned from the start if Milosevic does not gives it up, invasion of Serbia may or may not be deemed necessary, most likely it does not. Russia and China still likely not going to allow a UN mandate but slightly more likely to look the other way.
* Serbia does any two of the above. Most likely this makes Russia and China reluctantly leave Milosevic to his fate and concede a UN mandate for intervention, the Hitler analogy is now really flying in the eyes of the Western public opinion. Ground offensive in Kosovo is planned from the start if Milosevic does not gives it and occupied areas up, invasion of Serbia may or may not be deemed necessary, most likely it does.
* Serbia does all three of the above. In all likelihood, invasion of Serbia to enact a regime change is seen as necessary and planned for from the start.
As for the military and political outcome of ground invasion of Kosovo, in all likelihood NATO suffers losses comparable to invasion of Kuwait or Iraq. Once they prepare the necessary logistics in Albania, and smash their way through the mountain passes with tanks and artillery, they have an overwhelming advantage to the Serbian army in a conventional fight. The returning Albanian refugees are utterly sympathetic to NATO troops, occupation is not going to give any problems to NATO except in the Serb-heavy northern stripe. The justification to enforce Kosovo independence is clearer from the start, if NATO is any smart they partition Kosovo between Albania and Serbia to stabilize the region.
Conquest of Serbia itself is going to be somewhat more bloodier than conquering Iraq but not substantially more so, again NATO has an overwhelming conventional advantage in a conventional war. Management of occupied Serbia is going to resemble Iraq in some ways, some serious amount of nationallist Serb insurgency is possible. However it's not going to be as bad as Iraq since there is not going to be warring ethnic and religious groups fighting a creeping civil war. Again, a good way to mollify Serbian public opinion would be to partition Kosovo.
Such a different Kosovo War would have significant political and strategic long-term effects as well:
* European countries get increased motivation for real EU foreign policy and military integration, especially the latter. The nucleus of a real EU army may be likely created in later years.
* NATO has a favorable precedent for large-scale military intervention in Afghanistan from the start, which can change that war radically.
* Russia gets even more determined to keep NATO out of its perceived ex-Soviet turf. Expect full-scale invasion of Georgia to accomplish a regime change at the slightest provocation, and perhaps more determined attempts to foster separatism of Crimea. Most likely, however, it's not going to push for Eastern Ukraine separatism, or worse, messing with Russian minorities in Baltic states as this would be too much of a risk for confrontation with NATO (esp. the latter).
* There is a clear and successful precedent for large-scale humanitarian intervention. Sudan is one place where it is likely to be applied in later years, Somalia is another (esp. when Islamist insurgency takes root), Burma might be as well but China might threaten intervention to veto it in the latter case.
* Difficult to say how this would affect Iraq. It mostly depends on...
* Clinton ends his presidency with a clear major military victory. This could tip the 2000 election in favor of Gore, and spare the world the tragedy of the GWB presidency. Instead of the Iraq War, we'd see large-scale NATO intervention in Afghanistan, and perhaps in Somalia and Sudan as well.