Yes it's normal for some 3 year old children to wear diapers both day and night.
Not all 3 year old children wear diapers during the day because some 3 year olds are potty trained during the day and can use the toilet without the need to wear diapers.
Although some potty trained 3 year olds may wear diapers during the night to protect them against wet pants and wet bedding from bed wetting.
But then they wear underwear during the day and only wear the diapers at night.
Then some 3 year olds may not be potty trained at all for either pee or poop and will be wearing diapers all day and all night because they don't use the toilet.
Some children are not ready to potty train and be out of diapers until age 3 years and 6 months or even 4 years old.
Children will potty train at different ages and there's no set age that a child should be out of diapers and be potty trained.
Some toddlers will be ready as early as age 18 months to potty train while others may still be wearing diapers and using diapers until nearly 4 years old.
One of my sons potty trained at 18 months and was fully potty trained by 2 years old while my other son was not ready to potty train and wore diapers until 3 years and 6 months of age and was out of diapers fully by age 4 years old.