Obviously, you should really consult your doctor if you are worried.
However, I can tell you that my then 6 year old was hospitalised with an asthma attack a few days before our ski trip two years ago. He was released on the Thursday before we flew out on Saturday! The docs said it was ok for him to travel but to watch him and give him the ventalin inhaler a few times each day. As it happened, he was absolutely fine and had a great week skiing every day with no problems

. If anything, the dry clean mountain air seemed to help.
Naturally, his 4 year old sister did not like being upstaged and came down with tonsilitis on the trip - I lost a full day of skiing minding her

.