Winter in Italy

Check on idealista.it or immobiliare.it.
Both allow you to select the language.
They are the top choices to look for houses in Italy, both to buy and to rent. Airbnb usually caters to tourists who are interested in shorted stays (less than 30 days.
Below I tested idealista.it for both Palermo (historical center) and Syracuse (Ortigia). To me those are the most beautiful decent size cities in Sicily, and in winter you don’t want to be stuck in small towns where there isn’t much to do. Catania is not my favorite city in Sicily so in your shoes I would opt for Palermo (no. 1) or Syracuse (no.2). Palermo has more to offer for a longer stay, but with a long time at your disposal you could split your stay, let’s say one month each.
Be aware that unless you are a EU citizen you are limited to 90 days within a 180 day period (90: days, NOT 3 months), so if you go for 3 months you need to cut it short by a few days.

Here are Palermo and Ortigia. Ortigia is very small so choices are more limited (therefore pricier) but the rest of Syracuse will be cheaper if you expand your search. But both places show plenty of one bedroom furnished apartments for short term under 900€ a month.

https://www.idealista.it/en/affitto-case/palermo/centro-storico/con-arredamento_ammobiliato,affitto-transitorio/

https://www.idealista.it/en/affitto-case/siracusa/ortigia/con-arredamento_ammobiliato,affitto-transitorio/

We have stayed in Palermo the last 2 years in November. It was quite flat and with many interesting things to see. The weather was very warm and pleasant the majority of the time.

I would stay away from websites like idealista, in italy it is very common that whenever you rent an apartment, it is not in great conditions (excluding things like airbnb/booking).

I would rather search in airbnb, and then reach out to the property owner outside the platform (for example googling the property and finding it via google maps).

Most owners are happy to rent the entire property for a couple of months during low season.

It is less trouble for them as they just rent and forget for a few months, and in low season they are usually half empty anyway.

I do know someone doing this in Tuscany for example, I rented an apartment for very little money, and it was for a 3 months period around winter.

Do check the weather records for the period you are considering. Mediterranean Italy can be wet and not partuculary warm in Jan/Feb.

Hi Steven, you're preaching to the choir--

In February 2015, we met a couple that are Chicagoans like us, but both have US-Italian dual citizenship. And because the husband is a Rome native, they spend most of the winter with Rome as a base, but do some traveling around, either to Salerno in Campania, and to Bari in Puglia. We met them at a B&B in Salerno, and we became fast friends. In 2017, we spent a week in Rome near Campo de' Fiori, and visited them at their apartment, also the four of us took a daytrip to Orvieto in Umbria.

Late winter is an absolutely delightful time to visit Italy, central to south especially. I found the Roman climate to be very temperate, 45-60 F, and just the occasional rain. Best part is that--at least 9 years ago--there were few tourists and we basically had the run of the place. Restaurants, bakeries, lavanderias, attractions. We could open the windows wide and listen to Rome at night.

We will be revisiting Rome for 9 days next early March as a precursor to a longer winter visit in the next 2-3 years, for 4-6 weeks. I am convinced I can live more inexpensively--and better by the way--in Rome than I would as a snowbird in Florida, Arizona or Las Vegas. Things are quite a bit more pricey in March now than 9 years ago, but still a good value. In 2017 we paid $85/night for an efficiency overlooking the piazza, now we'll be paying closer to $200/night for a larger 2-bedroom place with high ceilings and many windows. I gotta have my fresh air!

Many ads on Idealista are from RE agencies. If you don't trust rentals by owners you can contact the agency advertising on the platform and request your options. My BIL and SIL used that method successfully in Portugal. Idealista and Immobiliare are the top sites used by Italians for vacation or any short term rentals of at least one month.

If you trust AirBnB more since it's an American platform, fine, but you will likely have to pay more for the rental.