I am just learning about semiconductors and this question arose. I can't find proper answers on Google.
Normal diodes work fine down to below 77K (liquid nitrogen). Below that, such as at 4K (liquid Helium) and below they often do strange things- carriers freeze out, they turn into oscillators, show hysteresis and so on.
Some specially made silicon diodes will work as low as 1.4K (we use them as sensors).