This is EXACTLY why I use the sleeping leopard variant rules in the DMG.
Slow pace is 200 feet per minute, 2 miles per hour, 18 miles per day.
If this represents 1/2 speed it's probably too far. Twelve miles per day represents a better 1/2 speed over good terrain for 8 hours of travel by foot.
It's not a trait of any particular creature. It's just my ruling on the general properties of being asleep, is that you aren't drawing any special attention to yourself.
not some random leopard that just happens to be in a cornfield.