If he has the same amount of troops? How shouldn't he be able to win if they have the same? Also, I doubt Ulfric lacks problems with supplies. It is Skyrim after all.
I'm talking about Tulius, not Ulfric the only advantage Ulfric has is that bandits don't attack nord caravans because every other caravan lead by another race is a target because stormcloaks don't care about them, as mentioned by a NPC in windhelm and Ulfric has the home turf factor whereas Tulius has to worry about Forsworn attack Imperial caravans and the harsh mountain paths leading into skyrim can end up being a trader's death from dragons, animals, bandits etc etc. The only real disadvantage Ulfric has is that he doesn't know how to save money and put every last septim in the Windhelm treasury and possibly the other Hold's treasuries into the war effort.
Histories greatest leaders have often if not always been good generals.
Exactly for instance George washington was a smart leader yet he was a terrible tactician but the point is you don't need to be a good general to pick good generals.