What clothes for a car journey and short walk

[AliveAndSleeping]

Ds is five months. Now that the temperatures are below 5C I usually put on a vest, sleep suit, snow suit (onesie type) and a hat on ds when we go out for a walk in addition to one or two cellular blankets. If he's just going in the car then it's two layers (eg bodysuit and sleep suit), a cardigan and maybe some trousers and a cellular blanket.

But when i have to pick up DD from school it involves a fifteen minutes car ride (each way) and the being outdoors for about twenty to thirty minutes before we are back in the car. You are not meant to put on thick jackets in the car seat

I just can't figure out what to put on a thick jackets in the car seat so I don't want to use the snow suit but nothing else seems warm enough for when we get out of the car. I really don't want to put the snowsuit on him after we've parked. It's a lot of faff for just twenty to thirty minutes. I have tried layering up with more blankets (ie a fleece km top of the cellular but he still seemed quite cold.

Any suggestions?

I have a 7 month old and a similar school run. In the car she wears normal indoor clothes (including a jumper/cardigan), booties, gloves and a hat. When we park I clip the car seat on the pram chassis and then add a blanket and her puffy jacket over the top like another blanket (upside down so the hood covers her toes well).

Other times when I don't want to use the snowsuit in the pushchair I put her in a jacket and a blanket under the cosytoes. Easier to remove in shops and cafes than a snowsuit. I only use the snowsuit for long walks.