My opinion is it is too cold right now. Unless your pool heater heats that water up. 3 or 4 months old is still very young. I swim my Yorkie all the time - you can see vids on here of him dock jumping and of swimming in the lake and or pool.
I plan on taking the pups to the lake this wkend but - Razzle if I allow him in (he is a full adult) it would be maximum 5 minutes or so.
Always start with the life jacket it allows their body to be in a better position for swimming and provides a measure of safety. Definitely show where the stairs are. And also I agree if your pup likes swimming watch out cause they will go to the water every single chance they get
