The College and the city arent a single entity, so I don't believe they get any of the enchanting money that keeps the CoW afloat. They have a single inn, so I dont think its people visiting to see the college either.

That being said, first CoW missions involves a massive excavation site. No magic in Skyrim implies it could be done solo or without physical labor. However no one besides Onmund the CoW apprentice ever mentions it, and we don't see laborers in Winterhold. The end of that mission involves a huge artifact being moved to the CoW as well, but again no laborers or mention of them.

So what can they live off? We see an inn, a general goods store, guards on patrol, and I think Ragvir(?) complaining that there's no available work. Is it the Jarl somehow funding everything from personal wealth? The collapse wouldnt affect the Jarl's coffers, considering no effort at all seems to have been put towards rebuilding.

The only quest in the area I recall are:

Azura's Star, which is more CoW business

Book collecting in the CoW

Mage Hunting for the CoW (might have been a mod?)

Bounty Hunting for the Jarl

Collecing an artifact for the Jarl

Stealing an item from the FH Mage for the Jarl's Mage

And maybe a Thieves Guild quest? (Is the bard in hiding?)

Just remembered there's a mage in the Frozen Hearth who might be singlehandedly injecting money into the business. Between his own "shop" and his living arrangement. So it is just wealthy people keeping their personal homestead going?

Jarl funds the guard

Guard buy goods from the inn and general shop

Inn gets money from the mage

Which keeps them buying supplies for the guard?

CoW occasionally has money move through the Mage in the Inn from passerbys looking to scrounge?

Jarl collects taxes?

CoW buys supplies from the single general shop in Winterhold?

Feel encouraged to make something up. Nearest I can think is that the local guards, while off duty, get hired to move shipments of enchanted items. And that's completely out of my ass, and potentially not lore friendly when you consider the town's attitude towards the CoW.