(Technically not furry, but everything I know about costume-making, I learned from fursuit tutorials.)
My son, for reasons which yet remain mysterious to me, insisted on being a Mr. Potato Head toy for Halloween. The commercially available costumes I could find looked like... well.. let's just say I wasn't thrilled with them.
Cue a frantic round of patterning/sewing/burning myself on hot glue, and here's the Tater Tot. I made everything except the hat. Foam body pod with fleece cover, foam and/or poly-fil stuffed eyes/nose/mouth/ears/moustache (all of which attach with Velcro and can be rearranged for the authentic Potato Head experience). fleece pants, fleece/foam shoe covers, and some glasses which were quickly whipped up out of presentation board and electrical tape, because really, this is for a 3-year-old and anything else would be waaaay too much work there.
Also, yes, the arms are permanently attached above the ears. The Spud laughs at your notions of anatomical accuracy. (Again... costume for a 3-year-old. Had to make it comfy or there would have been tantrums.)