Pressure decreases the melting point of ice, and applying pressure then releasing it will allow ice blocks to weld together by melting them and letting them freeze. See this video.
The detractors of this hypothesis claim that the pressure is 100 atm per degree C and thus too much to make it significant. Instead, the ice contact cold welds. Also, the warm room could help the metal wire melt through.
But reglaton isn't completely invalid. In the ice block case, the temperature of the ice is almost exactly 0 (the block is in a warm room and melting), so tiny temperature differences of 0.01C may be significant. For snowballs, the contact pressure is much higher than the hand-pressure because materials have much less contact area on a nanoscopic scale. In these "everyday" examples, what is the more important effect, regelation or welding?
To test this we could run experiments with a material like dodecane (melts at -10C), which contracts when freezing so does not show regelation.