Lois
I would rent before you buy. It’s difficult here in Portugal to get a long term rent however, in the winters it’s a lot easier. The nights can be very cold though. Central heating is not a thing they have and if they do it’s very, very expensive. I am currently sat here with my pellet burner on because it’s so cold outside and this house is not well insulated as none really are on the Algarve. On the Algarve, the houses are really built for summer not winter.
The other option is as MOnica wrote Motorhoming. The motorhomes have fantastic heating systems these days and can be very cosy.
I have heard however due to the amount of vans that some site in the Algarve are being closed as they are not licensed. The locals are cracking down. On Monday last, a site containing some 40 vans was shut and the toilets and showers had to be removed to a different part of the site. You would therefore need to be in and settled on a site for winter by end September. Having said that, September is the nicest month here in Portugal, just as the nights are closing in, in the Uk they become balmy here but don’t tell everyone as they will all be out!