Ice melting requires a listed GFP device, although the AFCI operates as a GFP device, its not listed for that purpose, You could use a combo listed afci/gfci, the trip level is 4-6 mA and may nusiance trip.
At our IAEI meeting this month we had a rep from Cutler Hammer Showing on AFCI's and I asked this question. He called me and told me that they do have a listing for this type of use. and the GFP in their AFCI is rated at 30 Ma.
I just got several new CH215AFIT's today and they were marked on breaker labeling as being listed for equip GFP as well as ordinary AFCI duty.
Looks like the newest stuff rolling off the line has the labeling to reflect this possible GFP usage. Good to know - the (Cutler) AFCI's are cheaper than a 30ma GFP breaker and more readily obtainable