Yes, polos will help keep legs warm. But they only provide cosmetic protection. They offer no support to the actual leg, just from nicks and scrapes from an excited foot. I use them on the flat, not sure I would use them jumping
Polos are less likely to rub the horses legs, so are a cold option if your horse has sensitive skin/legs.
On the flip side, polos are less supportive as they have no hard shell/solid support.
If you are going for polos, buy the longest ones possible as they'll give the most support. I find that polos that are too short/just under the normal length don't do much but protect from cuts.
Polos will keep the horses legs warmer because they cover more area.