When you take a very cold or hot bath how is that influencing your breath?
There is an adaptation to being submerged in cold water in mammals called the Mammalian diving reflex.  Have you ever noticed when you jump into cold water, or enter a really cold shower you take a big breath?  While not exactly correlated with the dive reflex, it shows that there is a neurological reflex of entering cold water.  Here is a brief overview of what can happen when you submerge yourself in cold water:


Lower heart rate - aka Bradycardia, slowing down the rate of blood pumped will decrease the oxygen requirement of red blood cells, which in turn allow organs like the brain to use oxygen. 
Smaller veins - aka Vasoconstriction, the blood flow in your fingers and toes is reduced, allowing more blood to be used in the more important organs.  Eventually the vasoconstriction will apply to hands and feet.  
Blood shift - this adaptation allows the submerged animal to dive without having their thorax to collapse due to increased pressure.  Not necessarily attributing to breathing patterns though, so I left the boring stuff out and paraphrased.


In hot water, the opposite happens with respect to #'s 1 and 2.  Increased heart rate, like when you go running, tends to increase breathing frequency.  Vasodilation allows blood to flow more easily and is primarily for heat exchange.  Have the warmer blood in your fingers exchange heat to the environment will cool it for the return to systemic circulation.  Surface area is a large factor with heat exchange.  Hope this provided some insight.