Can an employer demote you from full-time to part-time based on a medical condition that doesn’t prevent you from doing your job?

The issue is, if you work in the dry area, can you do your job--that is, the job the employer expect you to do, and all aspects of it--and do so without imposing unreasonable cost, effort, or disruption on your employer? And by saying that "I can't work in cold conditions," do you mean that you have a recognized medical condition, established or validated by a doctor, etc., or just that you are very uncomfortable in cold conditions?
If you have a proven medical condition and can do your job without giving up or failing to do part of it and without imposing unreasonable costs on your employer, they should have to let you work in the dry area and cannot take negative action against you e.g. reducing you to part time for having the medical condition. This would be a reasonable accommodation.
But if to work in the dry area, you couldn't do all aspects of your job, or were less productive, or would have to do a different job other than the one the empoyer wants you to do, or would be disruptive or costly to the employer, then they could cut back your hours or even terminate you. The employer only has to make reasonable accommodations that let you do the job they want you to do they don't have to make unreasonable accommodations, give you a different job, or accept only partial or less-productive performance.