It looks like searching for votes:-1 is:question does yield questions with at least negative one votes (when ordered by Relevance, the last few pages are all questions with scores of -1, though when they're ordered by votes, the last pages all have scores of 13 for me, which makes it look as though it is not working; perhaps this is a bug?) The Search Tips say of the votes option:

posts with a minimum number of votes votes:15 apples oranges

so it looks like there is not currently a way to search for only downvoted questions, since any negative search will include upvoted questions as well, but you can use negative values.

It looks like searching for votes:-1 is:question does yield questions with at least negative one votes (when ordered by Relevance, the last few pages are all questions with scores of -1, though when they're ordered by votes, the last pages all have scores of 13 for me, which makes it look as though it is not working; it looks like only the first 5000 results or so in the selected order are taken, so the last page will be positively voted questions, since there are more than 5000 of them without further specification) The Search Tips say of the votes option:

posts with a minimum number of votes votes:15 apples oranges

so it looks like there is not currently a way to search for only downvoted questions, since any negative search will include upvoted questions as well, but you can use negative values.