What can i do to stop the cold air from coming in the doggy door?

Is your doggy door a waterproof model or a weather proof model? Have you tried insulating it?

This might help: https://www.doityourself.com/stry/how-to-insulate-a-pet-door-flap

A piece of Carpet fixed to it..

Hard question to answer without knowing the style of pet door and if it’s installed in a wall, door, or glass door? Mine is installed in a wall and has a inside and outside rubber flap to help keep the cold air outside! If yours is in a wall and don’t have a second flap. I highly recommend buying a better model! In the long run a new one could be a lot less hassle then trying to make a old one air efficient blocking system? Good luck

Use a hairdryer to heat the plastic where it is bowed and then immediately place something solid and heavy against it. Leave for at least 15 mins. You may have to repeat it you didn't heat plastic sufficiently the 1st time.

Mine is in a wall so I had a 'mud room' built-just wider & taller than 'dog door' about 12-15" long w/heavy-double layer of denim at 'doorway'. Outside. Invent your own

Replace the flap. Sold on Amazon and takes 5min tops to replace. I've done mine twice over the past 10 yrs. Cost less than $25

Try the method of heating that Dawn suggested. I too have the kind that is winterized with the two flaps. We have four dogs that are constantly going in and out for the past three years and have minimal warping on one and the other still keeps the air from coming in. We just love this one. We have had the single door kind and had to put the stationary door up all the time to keep the air out when it was really cold out.

I have the doggie door that fits in my sliding glass window. On really windy days I have the same problem with the wind coming in. The door is in good shape, but just won't stay closed on windy (20-40 mph gusts) days. My husband built a box entry way to put on the outside that stops the wind (opening on the side). It, too, has a plastic door but is a wind breaker for the "real door". Good luck!

You could put up a double flap on the inside right over the top of the doggie door, something in plastic would work well. It may not look the best, but it will do the job.