Carseat & clothing

When my baby was born (December), I would dress him in whatever clothes he was wearing for the day, add a blanket and then had the winter car seat cover on top.

I think we’ll be doing the transition to the convertible car seat before winter so my question, how do I dress him knowing bulky things aren’t allowed under the straps ?

We have a MEC toaster suit for snow play but I obviously need something for him to wear in and out of the car/buildings etc.