Yes, if there is frost, then the temperature where the frost occurs (frost on the ground) must be at or below 32°F.
Okay . . . here are two possible explanations:
#1 - The "simplest" explanation is that at your location the temperature was actually at or below freezing that morning. While Metro Airport's official low was 35°F, many WAFB neighborhoods, especially those to the east and north of Baton Rouge, reported a light freeze that morning. The potential variability in temperatures across the WAFB viewing area is exactly why we show our Weather Watcher numbers almost every day. The airport is a "general reference" observation site, but when we get into the low to mid 30°s, a degree or two here or there can make the difference between a light freeze or not. (Fact is, the temperature difference from one side of your backyard to another can sometimes be a degree or more!)
#2 - Yes, it is still very possible -- and not all that uncommon -- to have frost on the ground even though the "official" air temperature only dipped into the mid 30°s. In fact, from an agricultural perspective, we typically use 35°F or 36°F as a guideline for the potential for frost. Frost with "official" temps in the mid 30°s is most likely to occur prior to dawn, under fair-to-clear skies and with winds running light-to-calm.
How? Because the "official" temperature is recorded roughly 4 feet above the ground level. But under clear skies and little wind, the temperature right at the ground level can be 2° to 4° (or more!) cooler than the 4-foot above-ground reading. Often the ground will cool more quickly than the air, especially if the soil is relatively dry. So, while the air temp at 4 feet might be 35°, the temperature at the soil surface may be closer to 30°-32°F -- enough to freeze any condensation (dew).
Bottom line -- if there is frost/ice, it MUST be 32° or below.
Hope this helps!
WAFB Storm Team