Create folder like the following and store events in them. Then you filter will basically pull events from each sub folder.
Events
-- Jan
-- Feb
-- Mar
Or your Event page type, add a EventMonth field as a drop down where editor can select Jan, Feb, Mar. Then index EventMonth field as searchable. Then you filter for search would be
+EventMonth;Jan;January
+EventMonth;Feb;February
+EventMonth;Mar;March