I think that the main reason was fuel and resources. According to the Database on
www.starwars.com (don't know exactly how it fits in the canon priority):
There is enough oxygen, fuel and power in an X-wing for a week of non-combat operations
They were preparing for a runaway with possible harassements from the imperials on the way. using the X-Wings for the battle or any other patrol would have had them unprepared for a possible long and dangerous journey.
Also it seems that the snowspeeders were upgraded with armor plates from Y-wings, making them tougher than a X-Wing.
If someone can help me with a comparation, there could be another reason for the use of snowspeeder. The official site states that the snowspeeder is extremly maneuverable, while the X-wing has the atmosferic behaviour of a T-16 Skyhooper. Which one has better maneuvrability?
Also the small number of X-wings fighters could have some importance ... you can not use a snowspeeder to fight TIE-s. Thus they didn't want to risk their spacefighters.
Another reason that pops in my head is that Alliance technicians had to modify the original airspeeders for use in the cold enviroment of Hoth . It could be possible that the same modifications made on an X-Wing could affect their effectiveness in spacefighting.