Lithium batteries are much more tolerant of very cold temperatures but their death curve (that point where power drops off then plummets to nothing) is quite steep, and therefore during heavy use they can be unpredictable, so spares should be taken. A lithium battery is installed in my Sekonic L758, and two spares are to hand at all times in the kit.
Meters are frequently subjected to hot and cold conditions so they can be useful, if costly. Unless there is a profound malfunction of the Pentax spotmeter, I would imagine you can use any battery. Obviously, if you used the wrong battery, it may not start, may freeze, fail to meter or even short out. Look inside the battery compartment/chamber for any clue as to what batteries you can and use and those you should avoid.