I have a bad back (weak lower back from a hereditary spinal problem) and so weight was a big factor. My pram was around the 7kg total weight. Add a 20kg toddler/preschooler and pretty much that's the maximum that I can carry up/down the stairs on the train/tram/bus.
Also, with our first two children I didn't drive for 3 years, and again when we moved to Switzerland with the third - he was 8 months when we arrived, and is 3.5 years now. So most of my pram use is with walking and public transport.
A big sun/rain shade is a factor for me too...little babies hate having the sun/wind/rain in their face...
So, as a third-time mum, my pram is very light weight, umbrella style, and I managed to find one that almost goes flat, and I actually hand-made a padded mattress to go in the pram. When we arrived in Switzerland, for that first winter, I bought a second-hand baby sack for 9chf. Worth about 90chf, and it did us just fine, but if I was going to have a winter baby, then probably I'd end up carrying the baby in a pouch on my body, because I'd be too bothered by overheating/cooling all day...
Actually, our third child barely went out in the cold because if he was too warm he'd cry, and if his hands got cold, he'd cry!
My other advice is to get a pram that actually fits down the aisle of the bus/tram/train, if you are a regular public transport user - ours does and it certainly has solved lots of problems when people are in the way, or there are too many prams in the pram area, or the door isn't working properly!
About 50% of the time in Zurich my tram would not have level access, and I'd be pulling the pram up/down the stairs... having a narrow/light pram makes a big difference!
At work we have a super chunky pram which is perfect for hauling through the snow. It's actually really hard work pushing a pram in the snow, but our light-weight one has done all conditions, and the advantage is that it's easy to pull back out and over the embankments, rather than getting bogged