I don't know about coating the tank with veg oil, so can't really comment on that.
We keep the water running into our tanks all the time during winter. Just barely running, more than a drip, but far from gushing. That keeps them from freezing, or from completely freezing at least. It also keeps the hoses/lines from freezing up as well. It can tend to make a bit of a mucky mess around the tanks, though. So we have a PVC pipe coming off the drain that drains the water away from the tanks, so the water doesn't just overflow right there where the horses have to stand to drink.
This is a different system than we used last year, which was to bring one of those 5 gallon insulated drink containers (like you take to a picnic, or see on construction sites) full of almost boiling water to pour into the tank to thaw it. Ugh. What a pain, since I had to haul it from my house, in my truck to our horse property. Several times it tipped over and I had a mini flood in the back of my SUV.