Summary
You can't test positive if you don't take the test.
The freezing temperatures may be too cold for COVID-19 tests.
The federal government has started shipping free at-home COVID-19 tests
"The cold weather can absolutely have an impact on testing," said Dr. Nathan Ledeboer, medical director of Medical College of Wisconsin clinical labs.
He recommends following up with a PCR test.
Test kits have a built-in mechanism to show if the kit fail
Source
WGAL is an NBC-affiliated television station licensed to Lancaster, Pennsylvania, United States and serving the Susquehanna Valley region. The station is owned by the Hearst Television subsidiary of New York City-based Hearst Communications.
https://www.wgal.com/article/cold-temperatures-affect-accuracy-at-home-covid-19-tests/38912228