Tracey, low humidity, dry air cools at much faster rate than humid air. You've problem heard people say ' when the sun went down, the bottom dropped out' and temperatures really fell.. That's because the air was really dry or low humidity. Conversely, dry air warms faster allowing for fast warm ups after a cold morning, for instance. So, then, a freeze condition is more likely to occur with dry or low humidity air.
When temperature and humidity are combined in another expression called the 'dew point', the role that humidity plays with frost or freeze becomes very apparent. If we consider a hypothetical example using 45'F as a constant, then varying the % humidity by 10'F increments yields a different result expressed in degrees F. At 30% RH the low is 18'F, At 40% it's 22, At 50%, it's 28, At 60%, it's 32, At 70% it's 36, At 80%, it 39, At 90%, it's 42 and at 100%, it's 45. So, if your humidity is running 60% or higher in this example, it will not freeze, but lower, it will. Here's a handy little site that you can move the slider bars up and down to better understand the relationship. Dew points are often used by TV weather people to predict low temperatures for their area.
http://www.dpcalc.org/