Our first Life Style Visit: We checked in, met a Broker, he took us to our Villa and got us settled in. He asked if we wanted to tour homes and we did. We set the schedule, not them. Not pushy at all. We spent three 1/2 days looking at homes.
They will give you a map. Jump on the golf cart and go explore. Have lunch at various clubs, play golf if you have time (we did not until our 3rd visit), visit each of the Town Squares (each very different). Be sure to be at the Square during happy hour and live music.
Either time of the year you mentioned is good. It's The Villages......it's all good.
Take time to look on the website and determine your housing expectations before you arrive. The homes range from $200k to $1mil. Big range, but planning ahead on this will help your home search significantly.
Good Luck

