First of all, this widget (unfortunately) works only on TouchWiz based ROMs so don't attempt to install it on your non-touchwiz device. (It may work on deodexed ROMs, though). Don't forget to make a backup before doing any of this stuff.
How To Install?
- Download a root browser and navigate to /system/app
- Find a make a backup of AccuweatherWidget.apk
- Download the Samsung Galaxy S5 widget
- Replace it with the old one and set the permissions to: rw-r--r--
- Reboot your phone.
You obviously need to be rooted in case to replace a system file.