I'm not eating much, but i'm on a vegetarian diet that i started a month ago and it's winter time, is it vitamin d deficiency?

Unlikely: It is hard to get symptomatic vitamin d deficiency just because you're a vegetarian. There are plenty of sources of vitamin d in some vegetables. If you eat dairy as well, then you're likely getting enough vitamin d. Plus, living in southern california (as it looks like you're in), you get plenty of sun so you get plenty of vitamin d conversion. But you can always get your level checked.

Vitamin ?: Vitamin d deficiency is not necessarily present because one month on vegetarian diet.For be sure about your d levels , your fp could check your lab, and you can have specific answer. You can start taking vit d 3.+ ca+magnesium, sunny at am(15 minutes).Also vitamin c is good on spring, have show to help for spring fatigue, add some vegetable proteins to your diet.