I guess tradition. The old inauguration date used to be on my birthday of March 4th. It was moved to January sometime early in the 20th century I think.
I suppose if they had decent weather, the crowds would be absolutely unmanageable.
Yes... before 1937, Presidents were sworn in on March 4th. The 20th Amendment, ratified in 1933, moved it up to January 20th because the extra two months after the November election gave a President who lost an undeserved grace period in office.