We would not use "difficult" with weather, rather "mauvais" or more precise adjectives: neigeux (snowy), venteux (windy), froid, sec...
By the way, "temps" meaning weather is used in the singular form and generally with the impersonal expression "il fait": "il fait un temps épouvantable !" (horrible)
"vivre" can mean "to be alive", "to stay" or "to experience something".
in the latter case, "vivre" can be transitive: "il vit une merveilleuse histoire d'amour"
Otherwise: tu vis à Paris, je vis (j'habite) dans un appartement, le chat vit sur le toit, la taupe vit sous terre...
In languages, there is no single translation. In French, you can't say 'Hello', you say either 'good day' or 'hi'. Languages aren't meant to work perfectly with one another and a fair use of interpretation is needed. Here, for example: literally 'We live of times difficult' from that you know that it's >>> 'We are living through/in difficult times'.
"Vivre" can have a direct object:
- je vis une situation étrange (a strange situation)
- je vis une existence modeste (a modest life)
- je vis une vie sensationnelle (an amazing life)
- je vis une passion dévorante (a consuming passion)
- je vis un enfer avec toi (hell with you)
- je vis une expérience nouvelle (a new experience)
It should be "we're living in difficult times." Without "in" in the English version, it's wrong. The same way that adding "dans" or "en" in the French version would make the phrase incorrect.
And I'm pretty sure a more literal translation of this phrase would be closer to "we're living of the difficult times" which I think we all know sounds really weird and wrong in English. But of course, languages don't work that way. We can't just translate word for word.