People from areas with winter and summer could count the winters passing to know how many years have passed. Have people who lived in areas where winter and summer have almost no meaning managed to count years? If not, have they used some other measure to count the passing of time, or even not paid attention to large time units at all?
As you have already observed, not all locations on earth experience the same seasons. Some locations have little change in temperature throughout the year. There are other indicators that appear in a yearly cycle. Many areas have more than just the four seasons experiencing a yearly rainy or dry season. The arrival of yearly rains or dry weather would indicate the passage of a year. Usually there are other weather phenomenon that accompany the change from wet to dry such as a shift in general wind direction.
Another common method to track the year is animal migrations Many animals have a yearly cycle to their migration pattern. The arrival of butterflies, birds or whales in an area would indicate the passage of a year.
For more advanced cultures astronomical observations were the ultimate method of year measurement. The Sumerians, Egyptians, Maya, Chinese and many other cultures made amazing calendars based on astronomical observations.
It's also important to remember that even in antiquity there were complex systems of trade that would allow the spread of knowledge. People at the equator would be made aware of the yearly change by the flow of trade from locations where the passage of a year is more obvious.
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It's worth noting that even for people who live on the equator, and quite aside from potential changes in weather, the position of the sun changes over the year and the stars that are visible also change dramatically from one part of the year to another.