Why does the signal to noise ratio decrease when using high ISO speeds (e.g 3200) when shooting at night with a digital camera?
The Signal to Noise Ratio (SNR) does not decrease when the ISO setting is increased. SNR gets worse because there is less light around at night, and therefore less signal. Also noise will be higher if you use a longer exposure due to dark current and other electrical sources.
The reason to increase ISO is to boost the signal before digitizing to prevent even more noise.
With a digital camera, upping the ISO rating is achieved by aplifying the signal from the sensor. There will always be some random noise, and upping the ISO aplifies this, to the extent that it can start to become noticeable.
Different cameras behave differently in this respect, with the general case that a larger, more modern sensor will have better results then an older or smaller sensor (So a full frame DSLR like the Canon 5D mkII will outperfrom an older Canon 20D or a smaller Canon IXUS)
When you increase ISO you effectively increase amplification of the signal from sensor. There is always some noise present in signal, so when you amplify signal you also amplify this noise.
I'm not sure, but i think amplification process itself may introduce more noise.
Also at night there is little light, so signal to noise ratio is worse - so noise is going to be more noticeable.
As Rowland Shaw stated above sensors differ in they ability to capture light and dealing with noise. In general larger sensors tend to perform better - they usually have larger pixels, which means each pixel gets more light. Manufacturers keep working on sensor technology so newer sensors also tend to perform better than older ones.