Tok[y]ys

I don't know if there is connect between snow and chance of precipitation but If not, you can just move that slider in game settings to the left when you are playing multiplayer.

In game it's impossible and it's a shame but as @K0rnholio said, you can use some external programs to that, I've got joy2key too and it's really good way to change it. You can choose button on steering wheel etc and it's works fine.

Hey, why do you need this pickup? Is there reason why? I think that game is mainly about trucks, you can play SP if you want to play with these cars.. And.. add more mods to multiplayer is bad, if you add more and more mods to multiplayer it will be bad for people who have low-end PC, they will have FPS drops and nobody want to play with lower than 20 FPS.

Have you tried reinstall the Euro Truck Simulator 2 ?