No recommendations on a thermometer–sorry.
I have a partially clipped (usually a trace clip) OTTB who I like to keep well blanketed since he’s not an “easy keeper”. Generally on 24/7 turnout but with access to our barn, which he will utilize when really windy or wet. Always has hay in front of him, but increase in the frigid temps as he’ll eat more.
Taking into account wind/sun/rain these are my general temp ranges:
40-50 = turnout sheet with no fill
30-40 = medium
20-30 = heavy
10-20 = heavy with hood + extra hay
Less than 10 = medium under heavy with hood and inside at night + extra hay
I change blankets during AM and PM feeding only. Tend toward letting him be a touch cold in the mornings rather than risk too hot in the afternoons.
Then I also have a yak horse who only gets his blanket when it’s below 20 and probably just for my peace of mind rather than a real need. He has a sheet and a heavy and I never use the sheet.