Nope. Your snake can not catch your cold. Luckily very few disease are zoonotic (transmits from human to animal and vice versa). The bugs causing your cold are not the same as the ones that cause respiratory infections in snakes
something you can get from snake (although so amazingly rare and really only in poor health wild caught): tongue worm. Just as horrible as it sounds.
Back when I was a teenager and got my first ball python (wild caught, covered in ticks/mites) I was reading a book on reptile care and it warned about the dangers of tongue worm (rare even in wild caught). Heehee.