It can vary between 4K, as in 4 degrees more than absolute zero to hot enough to melt metal. Sooo many variables and yes, the difference can be a cm apart Hence I wouldn't take any weapon made for non-space to space. The bow might have turned into molten metal or snapped after freezing.

So get your space faring guns today, Ares Space Predator only for 19.990,-
(bullets sold separately, if using wrong ammo, gun might malfunction)

But given that we're talking about a Troll standing outside on a Space Station playing ahab against an enemy space vessel playing Moby Dick, i'd just tell realism to shut the fuck up and go away to let me enjoy my awesome ^^

Indeed

The reason being that space is almost a vacuum and thus an amazing isolator.
You don't have to be afraid of ambient temperature there but you will have problems venting the heat and thus guns would be pretty useless after only a couple of shots whereas a bow would last longer.

Another funny idea about the space troll bow: how much force is applied to the arrow? The opposite force is applied to the troll, who transfers it to the ground. The problem here is that the ground is not anymore that huge mud ball we call Earth, but a tiny space craft. What if the force was high enough to signficantly alter the trajectory of the ship?

Note that it could also be used as an alternate propulsion if fuel comes to be missing

The acceleration of the troll and the spaceship would be negligible, because the ratio of their combined mass to that of the arrow is similarly preposterous.