For the prefix, use the day you were born on. For the suffix, use the month. If you're not comfortable sharing your birthday, use a random date— today's date, holiday, etc.

Prefix:
1. Rain(y)
2. Clear
3. Cloud
4. Mist
5. Fog(gy)
6. Snow
7. Frost
8. Storm
9. Drizzle
10. Cold
11. Warm
12. Sun(ny)
13. Pour(ing)
14. Windy
15. Breeze
16. Cool
17. Chilly
18. Blister(ing)
19. Shine
20. Monsoon
21. Hurricane
22. Blizzard
23. Hail
24. Sleet
25. Dew
26. Wet
27. Dry
28. Thaw
29. Flood
30. Blaze(ing)
31. Humid

Suffix:
January: blaze
February: wind
March: breeze
April: cloud
May: storm
June: blossom
July: feather
August: wing
September: frost
October: pool
November: flower
December: bloom

I'm Snowblossom.

Thanks to relatedwords.org again.