"Encompass" is much more formal. "Encompass" is sometimes used in academic writing and literature, but it is not often used in everyday spoken English.
If this sentence was written in a serious novel, then "encompass" would be acceptable. But it would be unusual to use this sentence in a newspaper report or an email about your holiday.
Also, this sentence is in the passive voice, and "the fog" is the direct object of the verb, so we usually use "by", not "with". Compare these two examples:
A thick fog surrounded the city. >> The city was surrounded by a thick fog.
The weather god surrounded the city with a thick fog. >> The city was surrounded with a thick fog by the weather god.