Many dictionaries mark words in definitions with a descriptive word, such as (archaic), (derogatory), (offensive). I've checked many dictionaries and seen nothing of this sort for "hovel".
However, just because definitions don't have these usage tags doesn't mean it's entirely neutral. To get an idea of whether a word is derogatory or offensive you would either have to get MANY opinions from native speakers, or do your own research of the contexts in which these words are used, while at the same time ensuring that your methodology is sound. As I can't speak for much of that, I've given given definitions to most online dictionaries I have access to to show you that in most cases the definition hints at something negative.
Notice, that in some cases there are multiple definitions, some of which seem neutral, while others are definitely negative. In most cases dictionaries list the more common usage with a lower number. Definitions that aren't numbered are the sole definition of a particular dictionary:
3:a small, wretched, and often dirty house : hut
a small home that is dirty and in bad condition
Cambridge Advanced Learner's Dictionary and Thesaurus
1.a small, very humble dwelling house; a wretched hut.
2.any dirty, disorganized dwelling.
Random House Unabridged Dictionary (dictionary.com)
1.A small, miserable dwelling.
American Heritage Dictionary
1.A hovel is a small hut, especially one which is dirty or needs a lot of repair.
2.You describe a house, room, or flat as a hovel to express your disapproval or dislike of it because it is dirty, untidy, and in poor condition.
COBUILD Advanced English Dictionary (Published by Collins)
1.a ramshackle dwelling place
Collins English Dictionary
1A.small squalid or simply constructed dwelling.
Oxford Living Dictionaries
(I encourage you to look at the example sentences at this link, they seem to me to be all used negatively.)
a small dirty place where someone lives, especially a very poor person
Longman Dictionary of Contemporary English
a small and dirty or untidy house
The only definitions I could find that didn't have an obviously negative connotation were the ones from Wiktionary.
From what I can tell generally its connotations aren't too flattering, though you can find instances of "hovel" meaning just a small or humble living shelter without the negative association attached to it. Sometimes it's all peasants or poor folk have, and it's their home, and home is a comforting place, generally. By emphasizing the positive attributes you can convey a positive image, which generally isn't one imagined by most people hearing the word alone.