Clarification.
Head gasket failure. VERY rare on the V6. If it does happpen, it is most likely down to using pure water in the cooling system for a damn long time and driving the car very hard.
As Mark says. Remove cap to depressurise system and you can drive a suprisingly long way (gently!) Water mixes with oil causing creamy mayo in filler cap AND on the dipstick.
Lubriaction properties of the oil are compromised, but not a concern unless driving long distances!
Oil cooler failure. Much more common, especially on pre 1998 cars. Post 1998 had a much better stainless steel cooler.
When this goes, the coolant rapidly turn from water, to brown goo, which block the radiator and the coolant pipes, resulting in a car that overheats quickly...and will cause HG failure if driven for any length of time that way!
Bear this in mind when considering...