You can't really pick it up, but after you see the flower you should talk to Basil and Ellen to increase your relationship with them

Talk to Ellen one day when it's snowing and then go to the mountain summit after midnight on the same day. You'll automatically go back to your farm starting at 6AM the next day. Make sure to tell Basil and Ellen about it.

This flower have random day for found it.

You dont can pick this flower you only can looking this flower,then you back to your house

Talk to Ellen n Basil, n you must be friend with them..
Approximately at 6 pm go to the top of the mountain mother hill .. And you will see that snowflake.

Before you looking for that flower, you have to talk to Ellen, Basil and read at the library about flower of happiness. After that, during the snowy day, go to the mother hill where the chedar tree is at 6 PM. You'll see the flower of happiness and then you'll automatically wake up at morning (you can't pick up that flower, though). Go tell Ellen and Basil so your relationship will increase.

If you really want that flower be friends with Ellen and once you are closed with her she will tell you about the flower. Now go to the mountain at 6:00 PM and you'll see the flower.