What you need to understand about Horthy is, though he was revanchist and sought to restore at least part of the extent of the pre-1918 Hungarian monarchy, he didn't have ambitions on par with people like Napoleon. And frankly, given the economy, production capabilities and military capabilities of interwar Hungary, it would have been hard to pull off anything ambitious.
The fact that Hungary buffed up in the OTL second half of the 1930s was almost solely thanks to Horthy allying himself closely with Mussolini's Italy, and later (once the war was inevitable), with Nazi Germany too. This is part of the reason why Hungary started adding a lot of Italian-designed military tech (e.g. Fiat light bombers and fighters, etc.) to its armed forces' inventory already during the first half of the 1930s, and had a lot of it by the time it started negotiating with Germany and WWII was on the horizon. Most of the home-grown Hungarian military equipment wouldn't be sufficient for reannexing bits of neighbouring countries on its own. In OTL, Horthy only really started making open moves against neighbouring countries once he was sure he had some tangible backing by the Axis powers. Both on a material and diplomatic level.