Assuming it's a one time thing.

1.  Create a formula field as "Outdoor "&{Notes}   (brackets are not necessary for a one word field, just included for clarity)

2. Change the field type or the new field to Long text.

3. Delete the existing Notes field.

4. Rename the new field to Notes.

It's not a one time thing, I would need this function to regularly update the field

Then just hold your formula field, make it hidden, to avoid 'double outdoors' transform to something like 
IF(FIND('Outdoor',Notes),Notes,'Outdoor '&Notes)
And when you need to update, copypaste whole formula column to your Notes

I'm sorry I didn't understand.

Your suggested solution seems only require me everytime copy and paste, no?

Yes.
Of course, you can write a script to add 'outdoors ' to all values, where it absent, and run it by pressing the 'Run' button in extensions. But I don't think it so much better and faster than just copy-paste column

Thank you, however, how could I possibly continuously add some texts? for example: now I want to add "outdoor" to all the records, but maybe i would like to add another "BYOB" text in record 1 and 2 (not all the records)?