There are a number of reasons why a house, when the thermostat is set for the same temperature, will feel different between the summer and winter.
The location of the thermostat has a lot to do with it. Since it's normally located on a central wall it doesn't reflect the heat or cold pressure on the outside walls, which can make a significant difference, especially in an older, poorly insulated house. Unless it's a well insulated home, the temperature at the thermostat may be several degrees different than the temperature radiating from the wall.
Windows also have a lot to do with it. Older, leaky windows that cause cold drafts in the winter also cause warm drafts in the summer heat. Walk up and place your hand on an old, single pane window on a sunny, 90 degree day and it will feel much different than the same window on a cold 10 degree day. That temperature difference radiates into the room and can make a room warmer or colder than the temperature near the thermostat.
Add to that cold, unfinished and uninsulated basements that radiate cooler air up to the main floor of the house and help keep the floors colder in winter, poorly designed HVAC systems that don't control humidity and don't get proper air flow to all the rooms, and little or no insulation in the walls, ceilings and floors. All can combine to create a house with very poor climate control that makes 68 in the winter feel cold and 68 in the summer feel warm.