I know there are not that many sites--very few--that cover the informational guidance on the maintenance and technical difficulties of evaporative coolers, and so I feel compelled to share with you this very good, but rare, handyman site that does:
As you'll see, the link above has a section dedicated to evaporative coolers.
As to your specific problem of your cooler's blowing hot air, yes, the humidity is listed as one of six (6) possible causes of this cooler problem. To find out whether the other five causes are applicable to your situation, here is the direct link to the diagnostic article on hot-blowing coolers:
You should be able to review this article, and, one by one, determine what causes listed therein are not affecting your cooler in order to ultimately end up with one remaining listed cause that is the likeliest cause of your cooler's failure to blow cool air into your house.
This should help.