I play tense negotiations. Opponent plays nullify. Does my warlord have to exhaust? Is exhausting my warlord count as a cost to play the card? Any rules reference? Thanks

Yes, exhausting your warlord is a cost, so canceling Tense Negotiations leaves your warlord exhausted.

RRG, p.5:

"Costs: The word 'To'

Many card abilities are presented in a 'do X to do Y' construct. In such a construct, the 'do X' aspect (preceding the word 'to') is considered a cost, and the 'do Y' aspect (following the word “to”) is considered an effect."

(So, since you exhaust the warlord TO cancel the effect of an event with Nullify, exhausting the warlord is the cost.)

thanks a lot, I figured as much but my rulebook was lost in a recent warpstorm