The Winter War told Hitler what he wanted to hear, that the Soviets would be an easy target. Their recovery and firepower in the second offensive should have told him that the initial impression of ineptitude was deceptive, but that wasn't what he wanted to hear.
Historically, the Soviets tried to correct the German misconceptions about Soviet military power in the months leading up to the German invasion. They took Germans on tours of aircraft factories cranking out mass quantities of modern fighters, for example. They probably should have shown the Germans mass quantities of KV1s and T34s in say May of 1941, let them take pictures even. The optimum situation for the Soviets was for the Germans and the west to occupy each other long enough for the Soviets to finish rearming and enter the war at a time and on a side of its own choosing, and revealing a couple of new models of tanks was probably worth risking giving the Germans another month to prepare for those tanks.
A later war with Finland would almost certainly reveal the new Soviet tanks, and almost certainly would make the Soviets look at least a little more competent. Would that be enough to deter Hitler, or would it just mean that Barbarossa was better thought out and prepared?
That's a tough question. A lot of people focus only on one front in the war and fail to grasp the large scale shifts of power from theater to theater that happened or could have happened in 1941. The leaders of the time were quite aware of those shifts.
Hitler was quite aware that in the short-term a German invasion of the Soviet Union would make a Soviet attack on Japanese-held Manchuria impossible and that would allow the Japanese to shift their power south. He hoped that the increased Japanese power would force the US to focus their naval forces on the Pacific, giving him time to prepare for the inevitable war with the US. That sort of worked in the short-term because the US was forced to move naval units to the Pacific and didn't build the fleet in the Atlantic back to pre-Pearl Harbor levels until 1943. Hitler figured he would long since have disposed of the Soviets as a major power by then and would be harnessing ex-Soviet resources to building air and naval power for the war against the US.
Obviously, that strategy overestimated Japanese strength and underestimated the Soviets and the US, but what other strategic choices did Hitler have in 1941? The US was going to enter the war. If it was focused on the Atlantic, the Allies would win the U-boat war sooner than they did historically, and be able to build up forces in Britain far beyond what any conceivable German attack could cope with. They could win in North Africa and build up to invade Germany. All the while, Stalin would be building up and waiting to pounce.
Ironically, the victory in France painted Germany into a strategic corner because it turned them into a threat to the Soviets and the US. At that point the Germans had to neutralize the Soviets, either by diplomacy or war.
Hitler gambled that he could knock the Soviets out of the war while the US was still building and was preoccupied by the Japanese.
Waiting was a losing game because the US and Soviets had more resources to build with.
Concentrating on the west and trying to knock it out was a losing game because the US was invulnerable to Germany and a 1941 version of Sea Lion was even more impossible than the 1940 one. Hitler really didn't have any better options than to attack the Soviets in 1941 that I can see, so I suspect he would have.