Generally speaking, these various gadgets offer no advantage over the OEM parts but often carry some penalty, in this case perhaps a shorter life or increased noise - the car manufacturers/OEM suppliers have enormous R&D budgets to ensure the best possible match and performance from properly specified parts, plus reputations to keep - which is the only reason why they urge us to use OEM parts - BMW or Ford are unlikely to go under if we buy replacement filters from elsewhere.....
The warm air in winter comment is interesting but only if you have an A35 or something similar, which could suffer from icing on the carburettor venturi at certain temperatures/flow rates and a lot of cars with simple carbs had two positions for the air cleaner intake, with
one near the exhaust manifold for winter.
But...as Tonyav says, cold air = dense air = more oxygen = more fire