GadgetGary, check if your system/thermostat manufacturer offers the sensor/lockout option. Carrier and Lennox both have it. I had Lennox at my previous house, Carrier now. The outdoor temp is displayed on the Carrier 'stat by pressing the temp-up and temp-down buttons simultaneously. The lockout temp is programmed on a setup menu accessed by holding the Fan button for five seconds.
The Lennox thermostat was nice. It continually alternated the display between room temp and outdoor temp, and recorded the daily high/low (auto reset at midnight). A submenu could report the accumulated run-time of low-speed compressor, high-speed compressor, and auxiliary usage.
The lockout setting depends on system performance (the "balance point") and personal preference. The only way to know for sure is experiment and observe the results. The indoor temperature will rise, although it may be very slowly, as long as there's more heat moving in than what's escaping. The ideal system would continually vary its output to exactly balance during normal operation.
My previous house had a slightly oversized system (3.5 tons for 1278 sq ft) and could easily recover a 10°F setback in less than two hours at 30°F ambient, and hold 72°F indoors with normal cycling at 25°F ambient. The Carrier now is closer to "proper" capacity for the house (5 tons for 2550 sq ft, but I have 9' and 10' ceilings so it's a proportionately larger volume of airspace). At 30°F ambient it takes about 4 hours, maybe 4.5 to fully recover the 10°F setback (the setback period is from 10:30 AM to 3:00 AM, 17.5 hours, but it ends up being about 14 to 15 hours when the adaptive-recovery start-time is factored in). Weather conditions have been drizzling/misty so it gets frosty fairly quick. Outdoor temps in the teens I don't think it could handle for a recovery, or hold a normal indoor temp without assistance.
My usage and daily schedule is far from the norm, so YMMV.