LotR -- Book 5 - Chapter 02 - The Passing of the Grey Company

[Encaitare]

is Theoden not equally guilty? After all, as both an old man and the king of Rohan

Remember, even when Theoden was under the influence of Saruman and Grima, it was still evident that he had some strength in him. He may be getting on in years, but he's hardly weak.

No not at all. In a warlike society, such as the Rohirrim, if the king is able to ride and lead the army to war, it is the duty of the king to ride and lead the army to war. That is part of his job description.

Also, this was to be a last stand of sorts, and knowing they'd be greatly outnumbered, the Rohirrim would need all the morale they could get. To be fighting alongside the king would probably inspire his men to fight harder. It's more heartening to have the king right there than doing what might be seen as hiding away where it was safe.