Actually the grinding sensation sounds more like something out of place(which could cause nerve damage & hence the coldness), have you had any ercent x-rays or knee ultra sounds?? Both would be best to show what's really happening.
I had dislocating kneecaps from age 10 & after 2 lots of surgery on both they finally took the knee caps out at 19, that was 30 years ago & so I have experienced quite alot with my knees over the years & do have some knowledge.
Aside from the coldness & grinding are there any other symptoms? Lack of feeling anywhere? Difficulty kneeling or crouching? Pain anywhere or at certain times? Need to lay in certain positions for comfort or warmth - just to suit your knee &/or leg?