I was wondering the same: what is the difference between 'på høsten' and 'om høsten', if there is any? and also - using this opportunity :D - what's the difference between 'til høsten' and 'i høst'? i have a feeling that 'til høsten' means that something will happen before autumn begins, and 'i høst' - during the autumn, but i'm not sure.... can anyone help, please?
I made some notes on this a while back, so I'll type them up here for you.
Om + bestemt:
Generelt - Om sommeren er det varmt.
Til + bestemt:
Neste - Til høsten skal jeg studere.
I + ubestemt:
Siste - I sommer jobbet jeg.
Nå + Snart - I høst skal jeg jobbe.
I'm not a native, I'm still learning, so it would be cool if someone could verify this or expand further if necessary. Also my notes don't seem to include anything about på, so I assume it's also just used for general like om? I don't know.