S13 oil pressure light on when cold out

[slipnslidin240]

So like last week it was pretty cold here in Chicago n my oil pressure light came on and stayed on so I parked the car n Tryed the next day same thing light flashed n stayed on. This week it's been warmer so gave it another try and it went right off. I drove the last 3 days no problem never saw the light. Today it's cold again and go to start the car bam same problem light stays on. I replaced the sending unit n oil pressure seems to be fine. Any one have the same problem with their ka?