Peripheral perfusion does reduce as you get older although bizarrely now in my dotage I find its not a problem any more. Compression clothing works by increasing blood flow around the tissues you are wearing the clothing. Thats why it is successful as a recovery aid, so I can see the logic in your original thought. They rarely provide any thermal properties though so maybe need to be used in conjunction with something?
Many of the ideas given above should work but the general principles are:
don’t restrict circulation – wear shoes slightly larger/loosen laces/don’t wear overshoes.
maintain thermal barrier – wooden socks/wind barrier/proper winter shoes
start off warm – put shoes and socks in warm place (I use the radiator) before you put them on.
keep the rest of your body warm – layering the usual suspects.