Well one source of confusion is that north Americans use different terms then they do in the UK. I think what is typically called a vest in the UK is what we call an undershirt in North America. A babygro in the UK is what we call a sleeper in North America and a bodysuit in the UK is what we call a onsie in North America.
I think of a romper as a one piece outfit that is footless and not a sleeper. I would also assume a sleepsuit is a sleeper or babygro.
Anyway it really does depend on the baby. My DS was born the end of January in Canada (we had a blizzard on the way home) and i would put an undershirt or vest on him under his clothing (usually a sleeper or long sleeve onsie and pants) only if it was super cold outside. I then of course put on his outerwear (fleece snowsuit/jacket, hat mitts, etc) At home and for sleeping I would usually only have him in a sleeper and if it was cool during the day a sweater or hoddie over top at night a sleeper and then a sleep bag but we co-slept so he had us to keep him warm. He was a very hot baby and hated being too hot.
The rule of thumb is to dress baby in one more layer then you would wear yourself. Oh and as far as having the window open we usually have the window open a crack all year round, we like it cool when we sleep. The other thing to keep in mind is that at night you do not want baby to overheat (it is dangerous) so no hats to sleep in and I would prob but baby in a sleeper and a very light sleep bag if it is warm or if it is really warm just a sleeper or even just a onsie. Babies usually cry and their skin (arms and legs) get a bit blue and feel cool to the touch when they are cold.
I know it seems all confusing but once you have your babe in your arms and you get to know there temperament you will have it all figured out in no time

Just be an observant mama.