No, it's the flavor of 'nutmeg' (or something like that) won't carry over through the yeast.
However, it's common practice to step up when reusing yeast strains. Typically winter ales are higher in alcohol/hops compared to scottish ales...
If you heavily spiced the beer, it may have also had negative effects on your yeast just like high amounts of hops or alcohol. If you had high amounts of any three of these, I would suggest just buying a new vile of yeast.
1. BCS - Wet Hopped West Coast Blaster
2. CYBI - Gordon's IPA Clone
3. BCS - Scottish -80
4. BCS - Specialty Saison (Gold Medal at BMO)
1. BCS - Janet's Brown Ale (Fermenting)