I believe when this happens where I work (although it doesn't affect me, so not 100%), the part time staff are given the equivalent amount of holiday within their allowance to use at a different stage, as, like you said, it wouldn't be fair otherwise. Assuming of course, the full time staff are not being forced to use their annual leave and the day is being given for "free" essentially.
For bank holidays, part time staff should be given a pro rata as leave whether they work those days or not. But if it’s just they’ve decided to close on that day, then it’s discretionary leave and they don’t have to offer it to everyone.
We get pro rated holiday and bank holidays. So it doesn't matter that it's Xmas.
I think if the office closes over Christmas it’s counted as discretionary leave if any of those days falls over your non-working days then that’s just tough. You wouldn’t get an extra days holiday. Or you certainly wouldn’t where I work
Are you saying that they the full time staff are getting a free paid 1 day off (not being forced to use their annual leave), and that you should also be offered a free day off too for one of your working days, because in effect this is like a bonus? Or that your employer is shutting the office on that day and everyone has one day leave deducted from their a/l which would not affect you, just to get it clear. If it's the first scenario could be seen as unfair, if so have you approached your manager/HR for clarification? I know some smaller or private firms offer Christmas shopping days etc, check the companies policy too.
If it doesn’t fall on your normal working day then no it wouldn’t be classed as taken for holiday for you as you wouldn’t normally work it