is my AC covered by warranty on my 2010 Jetta TDI?

That's a good indication it is low on refrigerant. A warranty won't cover a consumable like that. You might be able to recharge the system with a can of "AC Pro" or equivalent found at any auto parts store, but I'm not a big fan of those, take it to an shop that does AC work and have them recharge it, should cost around $15 per pound.

its preaty common for a ac system to lose gas over long periods of time. Its usually recommended to have your entire system discharged and refilled at the shop they suck out all the old and refill with new. i would check for leaks tho since most often a reason for low coolant in the ac is a leak. Check the grill in the front of the car for dark spots that look like oil was comeing out of it it will indicate a bad coolant grill.