For comparison, after forgetting to update TPMS codes during seasonal tire swaps at home, my Prius has gone several trips of at most a couple city miles each before giving the TPMS warning. My Forester has gone 8 mostly highway miles on a single trip before warning. I haven't done it enough to have any clue if these figures are typical, or just small pieces of a very wide variable spread.
With the cold weather, I've seen the TPS come on as expected but I also have my upgraded ScanGauge reporting the tire pressures. Cold related, I monitored the warm-up and subsequent increased tire pressure. Then the TPS would go out. But Saturday, the TPS light did not come on even though the tire pressures were as low as they'd been the day before. Curious, it is not a show stopper since the ScanGauge provides much better metrics. Bob Wilson
100 ft might not be far enough if there are no other competing TPMS signals (Bluetooth) nearby. PVT for TPMS equipped tires: Tire Pressure vs. Temperature
TPMS is not a Bluetooth system. Bluetooth is bidirectional on a 2.4 GHz band. TPMS is unidirectional on 315 or 433 MHz bands. The TPMS sensor's coin cell battery could not possibly operate Bluetooth for any useful length of time.