Why do I have to heat the house to a warmer temperature on cold days to feel the same?

Your radiation environment (walls, windows) is colder. You are therefore radiating more heat, according to the Stefan-Boltzmann law:

Intensity I = σE(T^4-Ta^4), where T is your skin temperature and Ta is the ambient radiation temperature (as distinct from the air temperature).

Those fourth powers can result in a surprising change in radiated intensity.

Consider a small change in the wall temperature. Suppose your skin temp = 80 F (300 K). If the wall temp = 60 F (289 K) you radiate about 66 W/m^2. Lower the wall temp to 45 F (280 K) and the radiant intensity needed to maintain 80 F on your skin jumps to ~111 W/m^2.

And the windows intensify the effect since they expose you to the larger change of the outdoor ambient radiant temperature.

Having just replaced the Windows in my house (most were original and ~160+ year old, so it's wasn't fun, but it was interesting) I'll relate my experience.

The air flowing through your poorly insulated and sealed house is what causes you to feel colder when it is cooler outside. You may be at 60 degrees, but you have ~40 degree air coming in as your 60 degree air escapes.

Also, try measuring the temperature at the floor and at the ceiling... When it's 60 degrees outside, chances are that the entire mass of air in your house is going to be close to 60 degrees. If it's cold outside, your thermostat can read 60 degrees all day, but your feet can be very chilly.

My advise, besides fixing air leaks of course, would be to get a ceiling fan to circulate the warm air down from your ceiling and keep your feet warmer.

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I think kirchwey's answer is very close to being correct, although I do not like the idea that you are "radiating more heat," I think it would be better to say that you are receiving less radiant heat from the walls, floor, etc--since presumably your body temperature is the same both days. You may also have more latent heat loss if the air is drier and more convective heat loss if it's breezy.

You might check the radiant heat loss by getting an IR thermometer and pointing it at the walls, floor, etc., and seeing if they at a temperature appreciably different to those days when you feel warmer.

The air temperature sensor for the heating system is closer to the heat source than you are. As heat loss to the outside increases, there is a greater temperature gradient from the air temperature sensor to the outside. The result is that you are indeed standing in colder air, even though the thermostat is working properly.

air movement can make it feel much colder. and if your moving in and out of wamr and cold rooms, your body needs to warm up inside aswell as out, and this takes time. you might benifit from resealing your windows. i know i did, i have double glazine, and the seals were all terrible around the windows. i managed to get some sealers from a DIY store and just peeled off the backing tape and stuck them all around the windows. no more drafts. then i got some silicone sealant and sealed around the windows, and put some draft excluders on the bottom of the doors. made it much warmer. the problem is that if air is coming in, then something must be going out, all the warm air is going out as cold air comes in. but i believe that in the winter, your capiliries shrink so they hold onto more heat, and so dont absorb any as easily either. just my thoughts, prossibly right, but possibly wrong. lol

it differs because the air inside is coming from the outside. its just being filtered before it enters your house. some days on really cold days, it doesn't filter as much because the filter is cold too... does this make sense???

It's because you have no insulation so the heat just escapes. I use to live in a similar place without insulation. The warmest place to be is upstairs as heat rises. More than likely the thermostat is placed upstairs.