Most skiers who require extra warmth use heated footbeds (insoles) rather than socks. Given you need clean socks daily (one would hope) then the average holidaymaker would need multiple pairs. I personally have never come across anyone using heated socks despite dealing with hundreds of people every season.
I can see why heated socks might perhaps be a better idea for cycling than these insoles: even though the wires are thin, if I don't protect my feet somehow, perhaps by routing them up through the shoe sides, there may be chafing with associated blister, after some number of pedalling miles. Still, cheap enough for experimentation, to see if heated insoles as a solution fits.
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