If you are looking for "Value" rates/season, you are limited to January through just before Valentine's Day, and then late July to Oct 1, and end of November to mid-December.
Mid-February through the end of March is actually "Peak" rates/season due to school winter and spring breaks.
If you want to go as close to your birthday as possible- go in early February.
It's OK to get a Birthday button if that's the reason for your trip.
In Value season, the park hours are shorter, the weather is more "iffy", and more attractions may be down for refurbishing. But the crowds are at their lowest and resorts rates are as low as they ever are.
For example- a standard room at the Wilderness Lodge in Value Season is $225/night, but $340/night for the same room for that last week in February (Peak Season).
If you MUST go for your actual birthday- just be aware that Spring Break has started, the parks will be a bit more crowded, and the resort rates will be quite high.