Full-timers typically can live very comfortably on $2-3,000/month. That includes travel, fuel, places to stay, food, vehicle insurance, medical, registrations, vehicle maintenance, etc. In other words, all living expenses that one would spend on in a regular house.
Snowbirders need to take into account what the regular house expenses are that you'll still have to pay while you're gone such as electric, gas, insurance, etc. On top of that you will then have travel fuel expenses, campgrounds, food and misc. Everyone is different in their home expenses and how they travel during the winter.
Basically you can cut back drastically on RV travel expenses by staying in much cheaper RV parks rather than one that has a lot of amenities. You could limit your driving distance (fuel) to get there, you could stay in one place for the entire time and get a better rate than daily or weekly.
Food expense should be the same as when you're at home. You will probably eat the same and if you're not one to go to restaurants normally then you don't have to go to restaurants while traveling.
Same for entertainment. Many folks do free things. That's up to you on how much outside entertainment you need.
So really, no one can tell you exactly how much it will cost. Everyone is different. You'll just have to do some figuring based on your finances. I will say that if you can get that RV and vehicle paid off you'll feel a lot better. With full-timers, especially, it's recommended that you be debt-free before beginning the new lifestyle. I would guess that the majority of snowbirders are not debt-free.
Start by calling some RV parks that would be possibilities for you. Then roughly calculate how much fuel to get there and back. Then estimate other expenses and you'll soon come up with a good approximate idea.
Good luck and hope you can get away during the harshest time of winter if only for 2-3 months.