In most facilities located in colder climates, the institution issues winter clothing directly to inmates rather than requiring them to purchase it through commissary. Coats, thermals, and cold weather gear are considered necessary items and are typically provided as part of standard issue in regions where temperatures require it.
If the facility does sell jackets through commissary, the price generally falls somewhere in the range of $20 to $50 depending on the quality, the vendor the facility contracts with, and whether it is a lightweight layer or a heavier coat. Commissary pricing on clothing items tends to be higher than retail equivalents because of the limited competition and the markup built into the prison commissary system.
The most accurate answer for a specific facility is the commissary price list itself, which your inmate can access through their unit or ask a staff member about. Commissary lists are typically posted or distributed to inmates so they know what is available and at what price before placing an order.
If your person needs a jacket and the facility issues them, there is no cost. If they need to purchase one and funds are tight, making sure there is enough on the commissary account to cover it before the cold weather sets in is worth planning for. Getting money on the account through MoneyGram or whatever deposit method the facility uses ensures funds are available when the commissary order window comes around.