Winter soldier trait reads:

Can he use this trait on opposing characters?

As well as can he use it on multiple opposing characters in one turn, as it is not a free action & it is not a action he is given.

you can not give opposing characters actions unless specifically said in the power like Mind Control.

I think you are reading his trait incorrectly.

This trait affects Winter Soldier's damage value. So you can have one of your own guys take a power action to bump Winter Soldier's damage up by one. Or if your opponent gets adjacent to Winter Soldier he can give his character a power action to drop Winter Soldier's damage by one.

Winter Soldier himself does nothing to activate this trait.

this trait appears to have been meant to allow opposing character to use it but it contains no verbage allowing them to do so. so, nope, only your can prevent forest fires.