I doubt that heat tape would dissipate enough heat to keep a barrel of water from freezing. It is designed to keep pipes from freezing, with the small amount of water in them. Typically, the target pipes are in a basement or other protected location. Of course, how cold it gets where you are would matter as well.
I use a bird bath heater in my bucket. I just drop it in the 5 gallon bucket in the winter and don't have ice in the bucket. The heater comes on at 35 degrees and cuts off at 45 degrees, so it heats only when needed.
I just ordered a deicer from Blain's (they're on sale!) I've seen heat tape used on 5 gallons but I really don't think it would be enough for 30.
Last year, I found that a half-filled 5 gallon bucket with nipples inside the coop didn't freeze until the temperatures stayed in the 20's during the day. Not sure how the cups will do since I haven't used those. This year, I decided that I don't want to haul buckets of water out several times per day on the coldest days and I might want to go somewhere over the holidays so I need to feel confident that the water will stay liquid while I'm gone. $30 is worth that peace of mind.