Whilst it's not a legal requirement for a company to pay travel expenses, it's good practice to do so and the fact that they're not and expecting a 6-hour commute to have what amounts as forced fun so close to Christmas too (when it's going to be very busy) is very unreasonable of the employer.
They absolutely can make this request and aren't being unreasonable in expecting you to work on this day-however, from a morale standpoint-they're really not doing a lot to boost it, are they?
It would be one thing if they said they were covering the travel expenses for this day of delightful forced fun (can you tell I hate this type of shit?) and paying overtime/giving time back in lieu-then it would fall into a reasonable request.
But to expect employees to pay out of their own pocket to travel 6 hours to play games and "enjoy" snacks isn't reasonable at all. The issue isn't that it's so close to Christmas. That's a red herring, I think. Ultimately, the 23rd is a normal working day and yes, they can expect you to work it-but is it really reasonable to expect employees to do this with zero reimbursement from the company?
What I'd be doing is totting up how much it's going to cost me to get there and back in fuel and time and then how much I'd be expecting in pay for that day-and then making my decision from there whether I can afford to lose the day's pay or not.
But your employer doesn't sound all that good, if I'm honest.