Presumably have influence holding large part of nail? (7)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

CUT ICE (as in “that doesn’t cut any ice with me” = to influence someone’s decision or opinion), containing L (abbreviation for large). I’m not sure why “presumably”, but the phrase always seems to be used in the negative so perhaps Twin means “that’s what it might mean in a positive sense”? The skin at the base of a fingernail.