You’re correctly identifying thermal mass as why they feel cooler to the touch, but this is mixed up in some incorrect and contradictory statements. You seem to keep changing your reasoning behind why tiles feel cooler to the touch.
The ceramic tiles in your house aren't really "colder" than you
This is incorrect, and why I replied to begin with.
Flooring is colder than your skin, regardless of the material, unless your floor temp is above 92℉ (33.5℃). You can measure this with a thermometer. If something is the same temperature as your skin you won’t feel anything - there’s no heat transfer. You could have a copper floor if it was the same temperature as your skin, you wouldn’t feel a thing.
[Ceramic tiles] also have a high thermal mass … they easily lose heat to the air.
These two statements are directly contradicting one another. High thermal mass means it takes a longer time to lose heat to the air. Given identical conditions, ceramic will take longer to change temperature than fabric. For example, if you opened a window and it was 40℉ outside, the carpet would drop in temperature faster than the ceramic tile. It wouldn't feel this way to your skin, but it could be measured with a thermometer.
That thermal mass is why tiles feel cooler than carpet. Your body has no issue warming the fibers in carpet next to your skin to the same temperature as your skin, it's harder to warm up the tile because of the thermal mass.