I know for which game you are talking about, and yes we plan on having different seasons in the game, not only on different zones, but on the whole map.
I don't know if that will have impact on your character as it is a bit hard to balance that, for example if you are in deep snow, to be slower, that would be a disaster for the open world PvP. Yes we can think of somekind of snow shoes, but they must be cheap in order for everyone to get them, because if they are hard to get, then the players that got them will have huge advantage on the players that don't, and I'd they are cheap for everyone to get them, then there is no point of doing it as it will be the same.
We plan on the different zones (snowy mountains, deserts, forests) to have impact on the mount you use. For example it will be more appropriate for you to ride a bear in the snowy mountains, than a horse, or a camel in the desert will be faster than a bear mount, etc etc.