Very common problem on early X5s, particularly in the ambient temperature ranges you were in.

Replacement breather design did not freeze up as much as the originals. If you just let it thaw out, I think it may happen again, whereas the replacement breather is more robust. Not sure when the design changed, I thought the 2003 had the new style but I may be wrong.

Do a search on this forum, and you will find similar stories.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue