Walking the Pentlands in winter - safety?

Was thinking of walking up Allermuir Hill from Swanston later this week - the weather forecast looks to be sunny, although with temperatures below zero the whole day, after a day of snow on Wednesday. What equipment/gear (if any) would you recommend taking for a snowy/icy hillwalk in the Pentlands? I've done the Swanston/Allermuir Hill route a few times in spring/summer, but never when there's been snow on the ground, so don't want to underestimate it! (Just checking since this has always felt like a fairly tame route in Summer/warmer weather - but pentlandhills.org says to take a survival bag/ice-axe/crampons 'as a minimum' during winter: would this be overkill for this route?)