In reply to HGTS:
Ultra makes some good points about temperatures and there are a lot of public-access scientific papers on the internet which describe interesting research. This is a nice one:
http://www.medscape.com/viewarticle/811238
As asthma is a complex condition with a whole host of triggers (mine are exercise, cold air and fungal spores), how your condition changes with altitude is specific to you. But most researchers conclude that provided you're well-controlled and have access to your meds, then you shouldn't have many problems. You may find that you increase your inhaler use, both during and after exposure to altitude (and not just in the immediate aftermath, but for weeks afterwards), but this shouldn't present any obstacle.
If, like me, you're not on preventative (steroid) medication, but just a bronchodilator like salbutamol , then the exposure to cold, low oxygen and increased respiratory exertion can leave you with some residual inflammation of the airways, making other triggers more potent. It might be worth speaking to your quack on your return if you're finding this, as a bit of steroid could help.
Being a fit asthmatic at altitude is still better than being an unfit non-asthmatic.