There is no bad time to visit a winery but the season will definitely affect your wine experience. Everything depends on what you are looking for.
Most people choose to visit wineries in the summer when everything is green around and the weather supports you to have outdoor tastings and walks to the vineyard. Besides, visiting wineries in summer means that you are going to meet and socialize with other wine lovers since, during this season, wineries are full of visitors.
If you would like to take part in the harvest experience, then you have to choose fall to visit wineries. However, here you should consider the fact that harvest season varies upon the country. The harvest season typically falls between August & October in the Northern Hemisphere countries such as Italy, France, Spain, Georgia, etc. When in Southern Hemisphere countries such as South Africa, New Zealand, Argentina, it is typically between February and April.
Here is the list of wineries you can visit for the harvest experience:
Talking about Spring and Winter, you should expect to have more quiet wine experiences, where you will be able to ask more questions during the tour.