Compensatory Day Off Considerations
Well, if they arrived in the morning of the 1st of January, you need not give a compensatory day off. If they were traveling for the entire day, you may consider giving one.
It depends! Many companies have a policy where they only provide compensatory time off if the employee is working (and not traveling) on a holiday or weekend. This is quite debatable, but yes, many companies follow this practice. Some companies even have a policy of compensatory time off against expenses billed, which can seem odd.
If your company truly cares about its employees, then you should consider these aspects.