I do not believe that developing the holdings has any effect. (Barring the very special case of being a nomad and stationing troops in your capital.)
Presumably your issue is the supply limit in winter, rather than in summer. In this case, I think that the best thing you could do would be to acquire loads of commanders with the "Winter Soldier" or "Shield of the Tundra" trait; and then make each one the leader of the
centre flank of a different army. (The buff to winter supply only works if the commander is leading the centre flank.) To "acquire" the commanders, you could use favor-invites (or favor-consort, if you're female and your religion allows it) - or you could join the finnish warrior society, level up to rank 3 or 4, and generate new commanders using the intrigue decision.
EDIT - Since the buffs to winter supply from commander traits are only +3/+4 and severe winter is -5, try to avoid stationing your troops in provinces that experience
severe winter. (Or, at least, don't use the full summer supply cap in these provinces.) Further, be careful about
summer supply in provinces that only experience mild/normal winter (-2/-3): in these provinces, if you have a winter commander then you might have more supply in winter than in summer!
EDIT2 - Have you tried building a fort in your garrison province? I'm not at all sure, but I think it might possibly count as a "holding" for the purpose of the supply limit calculation. It's cheap and quick to test, so it might be worth a try...