You can't really sleep off a cold virus or any other virus.
But when you do have a cold then sleeping is good for your bodies immune system anyway so it's still good to get plenty of rest and sleep when you do have a cold.
When you sleep you help your body recover from the cold virus and helps your immune system build up which then fights off the cold virus.
When you're asleep your body is healing and repairing itself and boosting your energy so getting plenty of rest is essential to helping fight of a cold much quicker.
Still you should take some cold medicine, stay hydrated with plenty of water or tea and use a humidifier in your room or home to add moisture to the air.
Within a week to 10 days or in some cases up to 14 days you should be feeling much better and be fully over your cold virus.