Wigs can be expensive, but they can also be very affordable. It mainly comes down to a few factors. The hair used can be horse, goat, yak, or human (price generally rising in that order). Wigs can be made very full or very sparse depending on how many wefts are stitched in. They also can be had ready-made or custom, there are even second-hand wig sellers in large cities like London. Basically, the price range is very wide. Advertisements even usually mention a range like 30 sh. to 3 pounds or 14 sh. to 25 sh. You can read a good amount about wigs in this research paper about wig making in Colonial America.

So, it could be afforded by anyone who deemed it important enough (which is definitely personal preference). However, they could have also gone with a wiglet (partial head covering) or a queue piece that ties about the head. Those can be much cheaper in price and more practical. Keeping one's hair longer is also an option as the hair is braided, tied up, covered by a cap, or kept in a wig bag most of the time. George Washington didn't wear a wig, for example, but styled his own hair.

It's important to note that the "powdered" portion you mention is part of the regular hair care and styling process and would be used for a wig or for natural hair. Pomatum and powder act similar to a deep conditioner and a dry shampoo. The hair is combed often to clean it and the process is reapplied every couple of weeks depending on need. It does not require powdering to the point of being white, that is a fashion choice that is applied after styling in addition to the regular powder amount. Colored powders also existed, including brown if one wanted a natural appearance. The Toilet of Flora has many recipes for haircare.