Your weather is quite similar to us here in England I believe.Most pet stores sell good quality coats being fur ones or rain macs , thats where I get Tias from.Like you say our weather can be unpredictable and just the other night I needed to put a t. shirt on Tia as it wasn't cold enough for the central heating to go on but she was chilly.I carry her coat in her bag every time we leave the house just incase the weather turns.I don't know how old your baby is but Tia is a year old and weighs 5lb so she does tend to feel the cold.I hope some of this is useful to you.
If you look at my avatar you can see her with her cosy jumper on lol