Depending on the topography or season, you use only one filter for air conditioners and furnaces. There is no need to change the type of filter with seasons. Instead, use an efficient filter compatible with your system all year round.
Another myth going around is that a thicker air filter is better. That is not the case. Using an air filter that fits your system makes the functioning efficient, not the kind of filter alone.
You can, however, change to a filter with a better MERV Rating in a higher allergen season to improve the efficiency of the HVAC system, as there are more suspensions in the atmosphere. A filter with a higher MERV rating traps more airborne particles like pollens, dust, and other debris particles, thus keeping the air in your house cleaner.
While you do not use a separate filter for both systems, changing it when the season changes are advised to maintain efficiency. As a rule of thumb, changing your filter every three months is reasonable.
Duraflow Filtration has the best collection of all kinds of Air Filters fit for your air conditioners, furnaces, microwaves, and all other appliances you need them for.