Can you ice a sprained ankle late in the healing process?

Depends if swelling: probably ice initially for first 24-48 hours and then warmth. But if continue to be swollen, ice and see a doctor for a more thourough examination, perhaps x rays or MRI or in need of a support.

Yes: Anytime it flares up during a return to activity, it becomes 'acute' again which usually signifies inflammation. Ice is best for that. At that stage you can ice for 10 minutes then do a warm wet towel massage to the area to help move the fluid along as well.