Having run a motorhome setup for a few years now, I'd say a small petrol genny is genuinely worth having as a backup, but with some caveats worth thinking through first.
The main issue with petrol units is fuel shelf life — petrol degrades surprisingly quickly, especially with ethanol blends. If it's sitting there "just in case," you'll want to either use a fuel stabiliser like Briggs & Stratton's treatment or run it through every couple of months. Learned that the hard way with a carb that needed cleaning out.
For occasional backup use, something like a Honda EU22i or the slightly cheaper Hyundai HY3000SEi hits a decent balance between portability, noise levels, and clean enough sine wave output for sensitive electronics. The inverter-type gennies are worth the premium if you're running anything with a battery charger — a Victron IP22 or similar will thank you for it.
Capacity question: what are you actually trying to power? If it's just keeping a Fogstar or similar LiFePO4 bank topped up during a prolonged gloomy spell, a 1–2kW unit is probably sufficient. If you're wanting to run heating, a kettle, and charge simultaneously, you'll want to size up accordingly.
Also worth considering: CO risk if you're tempted to run it in a garage or outbuilding with poor ventilation. Sounds obvious but it catches people out.
My honest take — borrow someone's for a weekend first and log what you actually need it to do before committing. The market is full of cheap units that sound tempting but won't last.
What's your current battery setup and typical winter load looking like? That'd help narrow down the right size.