Yes, hair is a body part for the purpose of spells.
I've searched the Player's Handbook for all references to 'hair'. Most references to hair relate to how hair contributes to your appearance or body (there is even a slot in your character sheet for hair). However, we want to see whether spells treat hair as a 'body part'. There are three spells which reference hair and body parts together.
If you have a body part, lock of hair, clipping from a nail, or similar portion of the target's body, the target makes its saving throw with disadvantage.
Body part, lock of hair, bit of nail, or the like
some hair, fingernail clippings, or other piece of that creature's body
The phrasing of scrying might suggest that 'body part' and 'lock of hair' are separate things, but this quote from the scrying spell comes from inside a small table where there was not room for any more words. It may just be that 'hair' and 'nail' are included in this brief list to highlight that these are valid and common options for body parts.
The phrasing of dream might also be read as suggesting that 'body part' and 'lock of hair' are separate things, but dream also categorised both things as a 'portion of the target's body'. By any plain English reading, a 'portion of the target's body' is synonymous with a 'body part'. This implies that hair is indeed a body part, and is probably mentioned separately because it is a very common choice of body part for the spell.
The phrasing for simulacrum further supports that hair is a body part, by equating 'hair' to a 'piece of that creature's body'. Simulacrum is notable in these three examples for not including the phrase 'body part' while clearly talking about body parts.
In conclusion, hair is counted as part of the body. Therefore, resurrection should regrow John's burnt hair, just as it would regrow his burnt skin and other body parts.
Thematically, this conclusion makes sense. Resurrection is a high-level spell which restores a dead creature to a fully functioning body (magical afflictions notwithstanding). It would be strange if resurrection would fix all wounds but not also fix hair in the process of restoring the body.
As a caveat, I will admit that there is some ambiguity in these readings. It depends on how broadly you define 'body part'. If you have a more restrictive definition of 'body part' than 'part/piece/portion of the body', then the logic above would fail. However, if you get to these kinds of semantics, then it will ultimately boil down to how the GM rules on these small ambiguously defined details.