It is a matter of time before human colonized Mars. For example astronauts aboard International Space Station(ISS) would celebrate Christmas many times a year due to the different time zones as it orbits Earth. Unless space colonists no longer obliged to adopt the culture they will have to agree on when X'mas fall on this red planet. I'm not debating whether religion is neccessary for thriving in space or on foreign planets, I assume early human colonists would carry on to adopt these cultures wherever they go even another world. How do we determine when should Martians celebrate their Christmas day does it have to coincide with inhabitants on Earth, if so what about the time delays for telecommunication signal to ping to and fro how do we factor those in?
I think it depends on whether you mean Christmas the religious holiday, or Christmas the seasonal holiday. Those meanings have been largely conflated over the centuries, and many people don't realize there are actually different things being celebrated here. (And, to be more accurate, there are many of each type of holiday that have been slowly merged into one date on the calender.)
The seasonal holiday is a break in the middle of winter, so the equivalent holiday should take place during Martian winter, if such a thing makes sense on Mars. It's unlikely it would, since Mars doesn't have snow or ice or chilly breezes or any of the other things we tend to associate with winter. The daily temperature swings are larger than seasonal temperature swings on Earth. (Says this space.com article.) As such, it might not survive the transition to Martian culture. Still, people invent holidays for pretty much anything, so I'm guessing someone would re-create the winter holiday if for no other reason than to get far more drunk than they should.
For the Christian holiday, it depends. Christmas is a celebration of the birth of the Christ. I could imagine that long-term Martian society would adapt a new calendar system based on the Martian year (in fact, wikipedia says it's already happened). At this point, you could just convert your age between Martian and Terran years with a factor of about 1.88. Then I would be 31.8 Terran years old or 16.9 Martian years old.
To the same effect, we could say Christ is about 1072 Martian years old and just put his birthdate somewhere in the Martian winter (or any other time of year, since it was an arbitrarily assigned date anyways).
On the other hand, people might prefer to celebrate it on the same day as Christians on Earth, and therefore end up celebrating it about twice a Martian year.
Any of those methods is perfectly acceptable, and there doesn't need to be any consensus between astronauts. As a religious holiday, nobody can tell anyone else when to practice their religion. As a secular holiday, well, the same rules apply. The mission comes first, but surely they would be allowed to take at least a few hours on whatever day they felt like partying/celebrating/being religious/being nonreligious/whatever.
If they are going to celebrate an Earth-based holiday, I would say the only logical time to do so is when Earth itself celebrates it. That means it'll fall on widely different moments in each year.
If people hang tightly to these old rituals, it might even mean that Earth-time will remain the standard as more places are colonized and that calendars will carry over.
In reality, I think they will probably stop celebrating these events and each colony will get their own rituals which are more in line with their new calendar. The people on the colony are likely to adopt their own culture when they are away from Earth.
Consider how Russia dealt with the adoption of the Georgian Calendar. In doing so, they did not adjust the Christmas date, which means they're celebrating it 'two weeks late' from a Western point of view. They'd argue that the West got the date wrong, of course.
So Martians who see Christmas as a religious holiday would be more likely to keep it on Earth time, possibly waiting for a clarification from the Pope. As for the time of day, that's traditionally tied to sundown/sunrise. Martians who are mainly secular would make it an annual reason to meet with family and exchange gifts which could go with the Martian calendar.