Walking feet - foot is best used to keep plaids from
shifting so they will match. You will never be able to
get fat layers to sew well with it.
What you need to do is trim out the fur. Cutting across
fake fur is done on the back through only the cloth
layer that the fur is attached to. But to trim out the
fur for seams or in this case to hide under a blanket
binding, it will be done from the top. I think I would
start by sewing the binding on one side only to the
lynx part and then trim the fur back to say 1/4" to
stitching. Maybe you could shave it. lol   Then fold
the binding to the back sandwiching the layers and
stitch again. You will need to take a tapestry needle
[needle with blunt point] to the fur caught under the
stitching and basically fluff it so it doesn't 'look'
caught in the stitching.
If I were you, I would try to practice on a scrap but
having said that doubt you have one. Let me know if you
need a scrap as I have some crappy stuff I used to
cover a cat bed and you can get a feel for the way it
works. Just a note, this stuff is a shedding nightmare.
All that trimming will be everywhere. If you can work
in the backyard or garage you might be happier. At the
very least work in the kitchen where you have tile and
not carpet.
Let me know about the scrap
Duckie

Well, I was thinking she was over on the Pac NW coast, but it turns out she
is in Spokane.  Her commercial website is http://www.specialtyoutdoors.com 
It seems to me that she has a personal site also, but maybe that's old info.  
She's really hepful answering questions on outdoor sewing on alt.sewing (i
know there have been several threads pinging penny s!)  I've been so busy
this summer I haven't followed any NG but this one, but there's a lot of good
help and good info over there.

I know Rainshed, have ordered from them often in the past.  They're good
folk. I maybe ordering from them again if we really get into cross country
skiing around here.  I wonder if they've gotten an 800 number yet.  

Not to take business away from them, but you can also get Malden Mills fleece
at good prices directly from them http://maldenmillsstore.com  (I loved to
drive up there when we lived in Boston.  Had to limit my trips due to limited
storage space! I still have a stockpile from their remnants table waiting for
a use.)  Also fabric.com has really good deals at times on Malden Mills
fleece, though they usually sell out quickly.

Kenmore switches manufacturers from time to time.  I once figured out who
made their machines in the mid-80s when I bought mine, but I've forgotten.  
Actually, I tend to think of mine as a budget priced machine, but $200 was a
lot more 20 years ago.  Now that I think of it, I'm rather surprised it's
that old.  I used to tell folks I have a Toyota of a sewing machine rather
than a Porsche, but then Toyota started putting their name on some sewing
machines and messed up my line.

I have been taking a class here
http://sewing.patternreview.com/
It has been an amazing experience. Called Rigid Handbag
with Kenneth King.
They have boards which I am sure are monitored.  I
peaked once into alt.sewing and quickly left.  Some
four letter words there I didn't even know.  Wonder if
it is better now.
Duckie