Where "cold starts" are a real problem, a common method is a small (for portability) battery kept on a "maintenance charger" in the garage, or where possible in another appropriate semi-heated area. You can then carry the warm charged battery to the device that needs a boost, and clip it onto the regular battery to get enough kick for an easy start.

Lugging a normal auto battery out from the barn is about as much hard labor as yanking a starter rope, but you probably don't need anything that large for what's been described.

For a generator of about the size suggested by your description you quite likely could use a motorcycle battery for the kicker, and the amount of boost needed wouldn't require more than AWG10 or 12 lead wires and small clips, so you don't have to fight with the #6 wires and battery clamps on a real set of jumper cables.

A good cycle battery probably will run close to $50 at common outlets at today's prices, and a pretty good maintenance (motorcycle) charger may be close to $20, but they should be easy to find, even if you have to go to WallyWart. A couple of years ago you might have found both for under $50 (US) at the same places.

An alternative might be to just hang a small (1 or 2 Amp) "keeper" charger on the frame of the generator and run a "permanent" extension cord to it. Lots of people use chargers of that kind to keep their motorcycle batteries up in the "off season" if they're "seasonal wussies" and don't ride them over the winter. Typical ones are about the size of 4 decks of poker cards, or even a little smaller.

John