This question and answers do a good job explaining why the Imperial forces didn't have fighter protection for their ground force on Hoth.
But nothing there explains why the Rebels didn't use X-Wings to easily dispatch the AT-ATs and buy more time. They obviously had them available because they were sending them off with transports and some of these were obviously not sent until after "defending" the base (since a few of the pilots of the X-Wings were the Rogue Squadron pilots fighting in the Battle of Hoth).
This happens in the EU in the book Isard's Revenge (in fact, the cover picture shows this scene) with great success and Wedge actually comments, on page 120:
Back then we were in airspeeders - undergunned and overmatched... Not the case this time [referring to being in X-Wings against AT-ATs instead of speeders on Hoth]
This indicates X-Wings can perform in cold conditions - there was snow in this environment as described by Corran Horn after he is shot down. The temperature difference between day-time on Hoth and here is unknown however.
Additionally, the X-Wings were able to destroy the AT-ATs with their laser cannons only - no grappling was required.
I suspect the answer is basically "because that would have been boring to watch on-screen" but it seems there may have been an actual in-universe reason outside of this.