Who's your service provider? I think AT&T has the lowest size threshold. TMO and some others send up to 995kb mms messages - that is including any text. If you're outside the U.S. I don't know your limits. So that is a very tiny video file. If you use the mms video setting you will get about a minute of very tiny res video. If you use the lowest res non-Mms video setting you will only get like 9 seconds. You won't get anything you can send above the lowest res. If you have ATT, unless they have changed their low threshold, you won't get but a couple seconds at the lowest resolution.
For email i have not had any issue sending video attachments. It may depend on your email provider or even service provider.
Also, you're not trying to send mms over WiFi are you? You'll need WiFi calling for that if your provider supports it. Otherwise you need mobile data on.