Dave Stewart used to record the Eurythmics vocals outdoors. Personally, I would argue that it's better to have no reflections than bad ones - and the ones from a small room with makeshift soundproofing are unlikely to be helpful. However ..... as James says, weather is the issue. You might think it's pretty still out, but the mic will probably say otherwise (as anyone with a video camera knows) - and whatever you do to reduce that noise will mess up the sound - whether its a fluffy mic cover (they are really expensive) or a windbreaker.
To put it in perspective though - a quote from top recording engineer Joe Chiccarelli: "I'll record anywhere. The best environment is where the artist feels the most comfortable and is going to give you the best performance. I've recorded in the control room, outdoors, inside live echo chambers, in bathrooms, on the porch, lying on the floor, in the closet..."
Spot on - the performance is 100x more important than a bit of noise or the wrong reflections.