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I am an Emergency physician with over 25 years multi-disciplinary experience.
I am going to be your expert in this question.
You may have had some 'frost bite' in the back muscle. Anything after 45 minutes may cause injury to the muscles and blood vessels
I would advise you to go to the ER, and let a doctor physically examine the area and determine if there is a chance you may have had any injury.
If it were in the extremities, then iit is worrisome, but in the lower back. Just go and get it examined, it is unlikely it will be anything major
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Based on the response, no it will not do any harm. If it were the extremities, then the approach would have differed. Just keep warm and go ASAP. In the morning