In this weather, I'd rather stay home.
'Preferisco' — pre-fe-RI-sco. Stress on the third syllable. '-isco' ending is first-person singular of -ire verbs.
Use on days of extreme weather — heavy rain, very cold, or oppressive heat. Italians take weather very seriously and cancelling due to bad weather is widely accepted.
'Con questo tempo' (with this weather) sets the scene. 'Preferisco' (I prefer) followed by an infinitive is a polite way to express preference. This phrase is honest and weather-related cancellations generate understanding rather than resentment.
Fa troppo freddo per uscire.
It's too cold to go out.
Direct — Italians are sensitive to cold and this is taken seriously
Con questa pioggia non si esce.
In this rain you just don't go out.
'Non si esce' uses impersonal 'si' — implies it's an objective fact, not just your preference
Afa da morire — resto in casa.
Deadly heat — I'm staying home.
'Afa' (muggy heat) is a very Italian summer complaint, especially in the south
Italians have a complex relationship with weather. While they love sunny outdoor life, extreme conditions (cold, heavy rain, afa) are considered legitimate reasons to cancel almost any plan. Staying in and watching TV together is an equally valid social activity.