Given what you described in the OP I'd say that in those circumstances you should definitely not take the time off.
It's a good paying job, in a field you're trying to get into, that *may* turn into full time. Insisting on taking time off for non-emergency entertainment, after agreeing to work over the holidays at your boss's request, or sulking when told no, are going to seriously sabotage your chances of getting taken on permanently. Even asking for the time off after saying yes is going to look bad. If would be different for something like a death in the family, or scheduled surgery, of course.
Now, if this is a bait and switch letter written from the *boss's* perspective, I would add that it's the boss's duty to be firm and bosslike say "No, you agreed to take the shifts, there's no one to cover you, and it's not an emergency. You can't have the time off". Giving a wishy-washy "Oh, well, if you really must" and then being mad at the employee is getting passive agressive, and sidestepping the unpleasant parts of being in charge.