I've lagered beers for 8 weeks and the beers carbed up just fine afterwards, so certainly cold crashing for a few days won't harm it at all. You don't have to warm up the beer to bottle, and you probably want to bottle it cool anyway as to not restir/resuspend the stuff that fell out in the cold crash. But you'll have to let them carb up at room temperature. It works perfectly!
What sometimes happens though is that people use "carbonation calculators" that ask for beer temperature. It doesn't say to use fermentation temperature, NOT current temperature! So, if you put in, say 34 degrees, it'll tell you to use like 1 ounce of corn sugar. Which of course means the beer won't carb! If and when you use a carbonation calculator, use the highest temperature that the beer reached during/after fermentation in that calculator. That will be most accurate.
I found that carbonation calculators never worked well for me, as I like my beer carbed pretty well (like at 2.4 volumes for most styles). So I found that using 1 ounce of corn sugar per gallon of finished beer worked great for me all of the time.
If you end up with 4.5 gallons at the end after the trub losses, then using 4.5 ounces of corn sugar (by weight) would be perfect. I have always weighed my sugar on my kitchen scale (I use it for hops, too), but if you don't have a scale that weighs to ounces you could use 3/4 cup of sugar loosely placed in a measuring cup.