Why last night when there was ice on the ground was my breath invisible?

For your breath to be visible when you exhale, the saturated water vapor in your breath must mix with air cold enough to reduce the mixture below the dew point, where the mixture is at 100% humidity. With ice on the ground the air above the ground could still be well above freezing (air can shift from a warm black parking lot pavement over a sheet of ice at the edges, etc.). And as you point out, the air could be relatively dry evaporating the moisture before it can condense. The initial air can be moist or dry at any temperature, with relative humidity between 0 and 100%. Even air below freezing has vapor pressure from the sublimation of ice (evaporation without becoming a liquid).