I did lots of searching on this topic, but I'm still confused.
I understand because of the chemical reaction in low temperature, it discharges very quickly. But, if you take your camera to a place where temperature is very low and use it for some time (maybe a week or two) will it decrease the battery's physical longevity in the future?
Will the battery performance decrease even after you return to use it in normal temperature (20C–35C)?
It doesn't discharge very quickly. Li-ion and other batteries actually increases the internal resistance and makes it discharge slowly.
As for your question, while keeping the battery on low temperatures can decrease capacity for some times. I don't think that it'll permanently damage your pack. You'll just have to recharge it again in "room temperature".
High temperatures, on the other hand, decreases the internal resistance and increases eletric flow, which will stress your battery. THAT can kill it for good.
P.S.: Some batteries can be damaged by very low temperatures, like the lead acid ones.
Source: taken from here.
EDIT: There`s also this great article on how to preserve your battery life, from ken rockwell. Take a look ;)
Nowadays camera batteries are (almost) invariably LiIon (Lithium Ion). There may be a very few specialised exceptions.
LiIon capacity falls as you approach 0 C - it's not that they discharge quickly as such, but that the capacity falls.
LiIon is unlikely to suffer permanent damage under charge or discharge down to 5 degrees C.
Discharge is safe down to -10C or -20C (manufacturers may specify one or other limit) but available capacity is getting extremely low by then.
However, LiIon batteries must not be charged in a normal manner at below 0 C and it is safer to only charge at 5C and above. Charging at normal rates below 0C can result in metallic Lithium being plated onto the anode. This is not removable by subsequent charge/discharge cycles and increases the risk of catastrophic battery failure due to mechanical stress or shock, and decreases battery capacity.
Batteries can be safely [tm] charged below 0 C but only at very low rates. For example, charging at -30C may be safe at rates 1/50th of normal maximum.
Most of the above information comes from or is given in the 'Battery University' article BU-410: Charging at High and Low Temperatures. Additional useful comment is provided there.