Dead of Winter exile PvP attack
The rules don't specify this, but you would not want to do that anyway, since you seem tot have the pvp attack rule wrong:


  If a survivor is chosen [to attack], roll the spent action die. If the result is equal to or less than the chosen survivor's attack value, ...


This makes sense, since the better a survivor is at fighting (low attack value), the harder it is to beat them (you have to roll lower). 

So you would not want to increase the result of this die. 

But suppose you wanted to do so anyway, I think you still can't. The rulebook refers to playing food cards when exiled to increase action die results, but if you are not exiled, you can only increase unused action dice as an action. I would assume that when exiled, this action becomes 'play a food card' instead of 'consume one food from the colony', but the effect is unchanged. The action die you roll for the attack is considered spent at that point (you used it to initiate the attack), so you can't increase it this way anymore. Also, spending food is an action, and it seems reasonable that you can't use one action in the middle of another (eating in the middle of a fight does not sound like a good idea)