I only acknowledge Character actions via the Party Order Thread. How that info gets there depends on if the Players collectively chose to have a Party Leader or if you are each Posting your individual actions.
The issue is not whether you can do it, but if you have time to do it - go to a location to look for a wild animal, catch the animal (How long will that take - an hour to a day?), skin it, hang to dry, then salt, then pack and so forth.
As a general rule, the World of Medieval is played as realistic as possible and not arcade style, so if the Party says they are going South and Rasputin says he is going to catch an animal then I can only assume that you will be left behind. I make no assumptions as a GM, I only go by Player Actions.
As a tip, this is why a Party Leader is good, the Leader can designate a time line: first we do this, then that, etc. When everyone is Posting their own actions it can become chaotic unless you plan first in Camp what everyone is going to do.