Fur handout is posted.
Elspeth Veale in The English Fur Trade in the Later Middle Ages talks about King John (England) wearing ermine, squirrel, and sable linings. His brother Richard apparently ordered that if anyone was captured wearing fur lined garments, those garments were to be confiscated and sent to the king.
There is fur in the Huntingfield Psalter (Pierpont Morgan Library. Manuscript. M.43 Oxford, England, 1210-1220)--the angel kicking Adam and Eve out of the Garden of Eden has a vair-lined cloak. Abraham entertaining the angels has a vair-lined cloak. Rebecca looks like she's wearing a vair-lined cloak.
The Lothian Bible (Pierpont Morgan, M. 791, Oxford, England, c. 1220) is a typically 13th c. style but no fur linings.
Harley 2799 (Germany, Arnstein, c. 1172) has fur. Solomon (f. 57 v) has a strip of fur over his arm which could be a cuff. His left arm is covered by his cloak so there's nothing to compare the mystery fur with.
Harley 5102 (England, before 1225) has fur as a cloak lining.
Yates Thompson 2 (Germany, Ottobeuren, between 1175 and 1200) has a fur something in the miniature of the Nativity (f. 57v). It could be the edge of the coverlet. The Magi in the Adoration (f. 62v) have fur-lined cloaks. Then there's f. 91v, which has a king with a vair lined cloak. The depiction of Felicitas and her seven sons (f. 103) has a plethora of vair lined cloaks.
So I have evidence for Margaret's potential use of fur, especially squirrel and especially linings, but not a whole lot, because it looks like the common artistic style(s) precluded the depiction of fur before 1225.