Average Fish tank heaters are not usually more than 300w and they operate (in a home environment) in a range of maybe 70-90degF. Not very economical in the long run to operate on a continuous basis as would likely be needed in a barrel full of
water in an outdoor environment with temps below freezing. Another option is a water bed heater wrapped around the barrel. I tried using an old 500w water bed heater on my 180gal Aquaponics fish tank in my 40-50deg house garage and it ran all the time to keep it in the high 60's (I didn't think to insulate the tank at the time). If the
greenhouse isn't insulated as is typical, to heat it with electricity you would need something along the lines of a modified electric
hot water heater element or hot tub heater of at least 1500w. Also when you go with electric heat of large wattage (over 1500w) it's preferable to use a 220v unit instead of 110v. Depending on how close the green house is to the electric outlet (unless you've actually wired it directly) don't try to run any heater on an extension cord unless it's a heavy gauge wire.
That said about electric heat. You could try to use a
solar water heater if you ever see
enough sun. But that might become more involved if the temps are below freezing often but it's doable. Or maybe a small
wood stove (rocket heater or ?) and a heat exchanger (copper coil, radiator etc) using thermosyphon action or a small
pump that would only be run occasionally to keep the water warm enough for radiant heat.
I'm considering these options for my
greenhouse aquaponics tank heating. My avg temps bottom in mid Jan at 41hi 21low so I'm leaning towards
wood fired heat with maybe
solar as a secondary system spring and fall.
It all depends on how much money you want to spend and how much unattended operation you want. The possibilities are almost endless.