Yes, a tent would have kept you warmer

• Tents block the wind and thus will eliminate wind-chill.
• While isolation of a tent is not good it will still allow your escaping body head to be trapped inside the tent and raise it's temperature by a couple of degrees. This will already make quite a difference.

The biggest difference, however, is that you should have used a proper, isolated sleeping pad. You mentioned that there was only a tarp between you and the snow: this means that your sleeping bag was compressed where your body weight was pressing on it and you had almost direct contact with the snow. You need a good isolated pad to combat this, there is no sleeping bag in the world warm enough to prevent that kind of energy loss in direct contact to the ground/snow.

That being said, please note that your sleeping bag rating is to be taken with a grain of salt, especially the lower end 'extreme' range: after all, what does 'extreme' mean? You barely survive but with arms and legs frozen off?

See also this question on How are sleeping bag temperature ratings determined?

Yes, a tent would have kept you warmer.

• Tents block the wind and thus will eliminate wind-chill.
• While insulation of a tent is not good, it will still allow your escaping body heat to be trapped inside the tent and raise its temperature by a couple of degrees. This will already make quite a difference.

The biggest difference, however, is that you should have used a proper, insulated sleeping pad. You mentioned that there was only a tarp between you and the snow: this means that your sleeping bag was compressed where your body weight was pressing on it and you had almost direct contact with the snow. You need a good insulated pad to combat this; there is no sleeping bag in the world warm enough to prevent that kind of energy loss in direct contact with the ground/snow.

That being said, please note that your sleeping bag rating is to be taken with a grain of salt, especially the lower end 'extreme' range: after all, what does 'extreme' mean? You barely survive but with arms and legs frozen off?

See also the question on How are sleeping bag temperature ratings determined?