Factual error: The Marine Colonel in Supergirl played by Eddie McClintock spends all of his time wearing Marine Officer's Dress Blue Bravos. Marine Dress Blues are ceremonial uniforms. On rare occasions, the Charlies or Deltas (no coat) may be worn as a work uniforms (the primary exception to this rareness being recruiters). The full uniform is certainly not worn for day to day work in the field.
Continuity mistake: While Kara and Alex are on the beach the sun on the floor changes between shots.
Answer: Another part of why the change was that it's cold in Canada in the winter and the old costume didn't protect her from it, whereas the new one is nice and warm.