If the weather is warm enough outside for the toddler to wear just a diaper then there's nothing wrong with that.
Also in the house that has heat during the winter and the toddler is gonna be warm it's okay then as well to let the toddler run around the house wearing nothing but a diaper.
I have a 2 year old boy that wears just a diaper in the house and he's sleeping right now in just his diaper which is what he prefers.
He takes off his pajamas and our house is nice and warm so it's not an issue.
Personally I find it very cute for him to be running around the house in nothing but his diapers and he's more comfortable that way.
I also have a 7 year old son that used to wear nothing but his diaper outside in summertime which was cute and he wore just diapers in the house most of the time as well.
It makes it easier to check if they need a diaper change too and you don't have to deal with removing clothes all the time either.
The 7 year old also sleeps in just the diaper at night for his bed wetting and he has become comfortable with me and his mom seeing him in just his diaper.
And his brother is only 2 so it's not an issue right now.
Sometimes he'll wake up in his diaper and come into the kitchen for breakfast and then get a shower before changing out of the diaper and going to school.
He only wears the diaper at night and doesn't need it during the day.
His 2 year old brother is the only one that is still in diapers both at night and day and probably will be for a few more years at least.