Gonna make a quick guide for this event for anyone who wants it!
find the tavern (the building with the chimney) talk to the bartender once you are inside and he will give you the first quest that allows you to obtain the other quests

then find the house shown below. the bird claw prints in the snow indicate that a delibird is inside of this house

interact with this box and a delibird will jump out of it giving you the first quest "The chase"

then speak with this lumbar jack to start your second quest. this quest will require you to find 1 piece of wood and 3 pieces of iron to help build his axe

next interact with this pile of wood to obtain the 1 wooden piece required for the axe


in this house we see more bird prints. enter here to find another delibird

in the same house interact with this man to receive the third quest which is to help find his master saitama

now speak with this lady to receive the fourth quest which is to find her lost snorunt

now come back over here where we find more bird prints and interact with the delibird inside

*****continuing in comments due to max images****
find the tavern (the building with the chimney) talk to the bartender once you are inside and he will give you the first quest that allows you to obtain the other quests

then find the house shown below. the bird claw prints in the snow indicate that a delibird is inside of this house

interact with this box and a delibird will jump out of it giving you the first quest "The chase"

then speak with this lumbar jack to start your second quest. this quest will require you to find 1 piece of wood and 3 pieces of iron to help build his axe

next interact with this pile of wood to obtain the 1 wooden piece required for the axe


in this house we see more bird prints. enter here to find another delibird

in the same house interact with this man to receive the third quest which is to help find his master saitama

now speak with this lady to receive the fourth quest which is to find her lost snorunt

now come back over here where we find more bird prints and interact with the delibird inside

*****continuing in comments due to max images****