In season 5, episode 21, Scare Master, Rainbow Dash is seen wearing a costume that appears to be a space suit of some kind:
This suggests that ponies have at least dreamed up the idea of space travel, though it doesn't necessarily mean they have developed the technology or magic necessary to actually pull it off.
In the show itself there does not (as of season 6) appear to be any further, more compelling evidence that might suggest ponies have access to space travel.
In the officially-licensed comics however things are a bit different, as there is actually an example of magically-assisted space travel in the main Friendship is Magic comic series, Issue #6.
In this story Celestia magically lassos the moon, and she and Luna use their powers to pull it closer to the ground:
The main cast are then able to tightrope across the lasso in order to get to the moon (except for Fluttershy, Rainbow Dash, and Luna, who are able to simply fly there):
It's up to you whether or not you consider the comics canon.