You can send and receive some short videos via text message - but to view video over the internet, yes, you would need a data plan.
And the LG Cosmos 2 has a 1.3 MP camera only, no video capability, so it's not the data plan that is preventing the cosmos from transmitting and playing video, it is the phone's software itself. If it did have video capability, you could send and receive videos via text message.
The Cosmos and Cosmos 2 do not support video - you will not be able to view videos on the phone.
The SD card would also need to be formatted for use in the phone, and all the info is erased during a format, so back up the info first (copy it to your computer). You'll be able to recopy the files into the appropriate folders once they are created on the card by the Cosmos. You can view the photos, but not the videos.