Is it normal to have cool air coming from under the house when ac unit is on?

This questions hard to answer without knowing what kind of AC system you have and where its located’ but here are a couple of thoughts. First if your air handle is under the house it may cool the air so you could feel cool air coming from underneath. Second your ductwork may run under the house ( I doubt it) this would also cool the air and if its leaking you may feel cold air blowing.

If you don’t know what your air handler is or want a general idea of how your air conditioner works check this out.