If the Dakota Territory was split east/west rather than north/south

[TDAS04]

No, East Dakota would still be Republican in presidential elections, but West Dakota would be more Republican.  Native Americans make up roughly 20% of the population west of the Missouri, and would likely provide the bulk of Democratic voters.  I could see politics polarized along racial lines, similar to whites and blacks in the Deep South.

Anyway, West Dakota would be the least populous state.  I'm pretty sure East Dakota would have 4 electoral votes.

[TDAS04]

While Republicans would win regularly in East Dakota on the Presidential level, local Dems would do really well on the statewide and congressional races. East Dakota would be very Scandinavian and Lutheran, sort of a more conservative and rural version of Minnesota. 

This is true, though things may be getting more partisan.

South Dakota was close enough in 1992 & 1996 that Clinton certainly carried the part east of the Missouri.  I believe that Obama lost East River to McCain by 3 points.

However, Bush & Romney handily carried both sides of the Missouri (even Sioux Falls isn't that liberal).  East Dakota gets even more conservative when the North Dakota part is added, and probably would not have even been carried by Clinton.

[TDAS04]

Is it possible to draw an Obama '08 seat in East Dakota with a population comparable to North or South Dakota?

The maps posted above basically would do it.

Come to think of it, it makes sense now considering that Obama outperformed Clinton in eastern ND.