Go into the template editor and open the templates which contain the logo. In the template you have to update the html to point to the new logo. Or just change the logo where the path is pointint to, that would actually be the better way to do it as it will update all templates that point to that location.
If you have created different editable sections for the email and landing page templates, you can make changes to one section in the template without impacting the rest of the email/landing page, and then mass approve the drafts. However, if you only have one large editable section, you'll have to make the changes in each asset one by one.
The easiest way is just replace the old logo file with new logo file in Images and Files section in design studio. You don't need to change in any template. Keep the same name for new logo file as old logo file and then replace the old logo file with new logo file in IMAGES AND FIELS.