http://www.jamstec.go.jp/frcgc/research ... _s.html.en
There are two types of El Nino, Eastern Eqautorial and Modoki. The strongest El Nino are Eastern Equatorial. Not all El Ninos have the same impact.
Here is a comparison between Eastern Equatorial and Modoki.
Temperature

Air Temperature During Eastern Equatorial

Air Temperature During Modoki
Both of them produce cool winters for Texas, but with Modoki, it is colder. Winter of 2009-2010 was a Modoki El Nino.
Rainfall

Rainfall During Eastern Equatorial

Rainfall During Modoki
An Eastern Equatorial is wetter across the equator, while Modoki is drier.
Here is a rainfall map for America.

Rainfall During Eastern Equatorial

Rainfall During Modoki
It is wetter in the Western US and South during Eastern Equatorial El Nino. However, during Modoki El Nino, it is much drier in the Western US, while South is much wetter. The wettest winter in the Upper Texas Coast was 1991-1992. It was the winter where there the massive Christmas 1991 Flood. That winter was a strong Modoki El Nino.
It shows that El Nino are all not the same. It does not mean it is always going to be wetter and/or cooler. Generally, for Texas, El Nino winter means cooler and wetter.