Possible, yes. The best option, possibly not.
The thing is that the motor requires 36v DC, and the generator is putting out 120v AC. You can get a AC-DC converter, and step it down to 36v, but that will add an extra component, and thus extra weight. It will also complicate the wiring. (although it looks like that particular model can also do 12v DC, but that would still require something to step it up to 36v).
Also it is important to remember that the electricity coming out of a wall outlet is MUCH more efficient than the output of a generator. The cost of gas compared to the cost of electricity is substantially different.
IMHO, you would be better off getting a battery pack (SLA or Lithium) and charging it off of a wall. Carry a charger with you, and if in a pinch you can plug the charger into the generator and convert some gas power into battery power.
As for carrying the generator with you for the freezer... It depends on the freezer. That thing is rated at a max of 120v at 1000w... seems a tad low to me. As it says on it, it's meant for fans, lights, small power tools. Freezers take quite a bit of juice since they usually have a pretty beefy compressor. If you have a particular freezer in mind you should be able to compare to make sure it's sufficient.
Also be aware of all the PITA rules involving food service. If it's a "just for fun" thing, then no worries, but if it's going to be an actual business, then you have a lot of requirements about temperature of the ice cream, having water available to wash hands and scoops, stuff like that (which might mean you have to haul water if there isn't water available at the location). But if it's just for fun, then probably not a big deal.
I think it's an awesome idea.
I actually thought about building an electric xtracycle that makes espresso coffee. I didn't think of using a generator, and was trying to figure out how to power it off of batteries and solar. I rambled about it on my blog actually: http://blog.oakwright.org/post/52819292 ... le-barista
Check out the thread where some folks piped in their thoughts when I was exploring the idea. There might be something useful in there for you: viewtopic.php?f=3&t=1280
I totally think you should explore this idea, and if you pull it off, I totally want to see pics!