Pardon the double-posting, but I decided to just try taking off the wire wrapping on my "free" bow. 

I got to looking at it when weighing the bow and measuring balance point.

a.) it was loose enough to move, anyway.

b.) "silver"?  Hah.  In a pig's eye.

So after looking over how it was attached, I took off the frog, used a pin to pull the end of the wire up out of where it went into the wood of the stick and unwrapped it.  I also had to peel up the "leather" a bit to get the end of the wire out after it was unwrapped.  "Leather" in quotes because it appears to actually be a bit of vinyl/paper stuff.  But that can be attended to later.

The wire was not silver of any sort, or even "German silver", which is a buzzword for nickel in jewelry.  It was some sort of rather springy steel.  I don't have a very precise scale, but removing it took the weight of the bow down by at least a couple grams.  It took no special tools, and it wasn't difficult to unwrap once the frog had been taken off. No thunderbolts, earthquakes or disasters happened.  I think the bow actually does handle a little bit better without it.  i can definitely feel the weight difference.

That would be the good points.  The bad points are that I am kind of used to the wrapping being there, and it feels a little odd without it.  I will try it for a couple days and if it still feels odd, I will wrap it with a bit of silk thread.  That would be fancy enough for aesthetic appeal and still not add anything near the weight of the steel wire that was taken off.

Comparing the "free" with my A. Breton, the balance point is closer to the head on the "free" by at least a couple centimeters.  I will play with it like this for a few days to see if that is a bad thing, and if so, I may scrape or sand a bit from the stick or even the head to get the balance to a closer match.  I would want to do that before attempting anything with fixing the camber anyway.

I must admit that I am rather surprised how much of a difference the removal of about 3 yards of thin steel wire makes in the weight I feel when playing, though.  It feels oddly "bare" right now without it, but that may not be a bad thing in the long run. I might get used to it, time will tell.

One other plus point.  When I had the frog off, I noticed that the wooden groove the frog fits into was rather poorly cut, and I cleaned up the edges of it a bit with an x-acto knife so the frog can move more smoothly.  I hadn't noted any problems from it, but I didn't like it being poor workmanship.

(Pic added of the "naked" bow along with my little A. Breton for comparison.  Note the rougher workmanship on the "free" bow from the wood of the frog being rougher to the varnish drip near the adjustment knob.  Also the rather crappy "leather".)

I do not think it is *just* for looks.

The author of the pdf, in the section titled "stripping your bow", mentions that the wire wrapping on the bow was developed about the same time as steel strings, in the first part of the 20th century.  It apparently did not exist on older bows made for playing on gut stringed instruments.

The actual effects that the metal winding has are gone into at some length in that section of the pdf.  Some of it is beyond my understanding and experience on a quick read-through.  Apparently it affects more than just balance, and he mentions it may be a good thing with steel strings.  But for gut or synthetic strings it may not be the best, or so I gather from the article.

On a really cheap "free" bow, I would bet that the metal winding is there in imitation of current popular bow design, and not something that was precision calculated for balance or anything else.  A good bow made by a knowledgeable luthier, I would expect that any metal winding would be an intentional part of the balance and other factors necessary to the functions of the bow, and I probably wouldn't go taking the wire off.

The "free" bow I am tinkering on has enough flaws that it is hard to tell for certain how much of an improvement it made, if any.  I can tell I like the weight better, but the "free" bow still feels clumsier and more "dead" to me.  But maybe that can be fixed, at least somewhat.  That is what I am trying to figure out.  Taking off the wire winding did make a difference I can feel in the weight.  But by itself, it was no miracle that suddenly made the "free" bow into a good one.  I still like my newer bow better.  I bought it because as soon as I picked it up, it felt light and alive in my hand compared to the "free" bow I had been using.