IMHO, i wouldn't let it ferment completely dry. I mean, 1.005 or so and i feel it's necessary to start protecting it from O2. it also depends on the wine. An apple, pear or similar has a much faster oxidation rate than red wine would. I would just error on the side of caution. if it stops early and it then sits in open air for 10 hours, that's not good. if you are around it most of the day and check it often (maybe twice a day), than it probably will be fine.
also, nobody has asked about the yeast. how are you storing the yeast and how old is it? what type or brand is being used? are you testing the acid? gotta keep your little workers happy or sometimes they'll slack on you! lol. some yeasts don't do bad in 60F temps. we've been keeping our winery in the low 60's and using lalvin 1116 for some wines without any issue. in fact wine temps usually gets up to 75-80F, so it's probably better in that case to keep it a bit cooler.
also, are you stirring enough? sometimes that can really help.
although, what others have said is probably right, i thought i'd put some other ideas out there. everyone does their own thing with wine and that's the BEST thing about it.