Looking back - mine were born in late spring/ early summer and were at about 5 months when the weather started getting cold. We live in a place where summers are incredibly hot and humid; it's definitely ok to be on the cold side, as opposed to being too hot. Don't feel bad 
I had a blanket under them for insulation when we went out. The pram/buggy sometimes got damp and the blanket (I think I used an old quilt) kept them from getting chilled.
At about 5-6 months they were beginning to start moving around on the floor indoors, and I found sweatpants plus sweatshirt, with a onesie vest underneath, was best for early attempts at crawling. When they crawled in their onesie sleepsuits they sometimes crawled up the onesie on the inside, ending up with their knees under their chins.
The early autumn was the time when I switched them into two piece clothing, and it made sense to bring them out in that too. I had several sweatshirts, some with zips in front, some knitted jumpers, some cardigans. Dozens of little onesie vests.
I got some little fleece booties for our trips, and always bought sweatpants a bit on the long side, with cuffs at the ankle so that their lower legs would stay warm. I also had a fleece one-piece pram suit with wide sleeves, elasticated at the cuffs, with a sleeping bag style bottom, and a hood. The wide sleeves were ideal for dressing as they weren't too tight. For the winter I had a snowsuit with ordinary lining (not fleece) and this made it easy to put on and take off too. Their hats were the kind with earflaps and they tied under the chin.