A lot would depend on what grade the IC chips and other components are rated at.
Some typical electronic component ambient temperature ratings (without thermal derating):
-Commercial, 0 to 85 deg.C (+32 to 185 deg F) which includes most home applications
-Industrial, -40 to 125 deg C (-40 to 257 deg F)
-Mil Spec, -55 to 125 deg C (-67 to 257 deg F)
The components and design the detector's mfg'er used can be reflected in the detector's advertised ambient operating temperature.
GeorgeSC is right about the batteries dependent on the batteries used.
Most off the shelf batteries are most efficient around 70 degF. Below 0 degF, most batteries discharge rate is severly degraded or stops functioning.
NiCad and specially designed Lithium batteries can function down to -40C but at a reduced discharge rate.
Some high end alkaline batteries can be rated from -20 to 54 degC such as the Duracell Ultra.
In addition, there can be a lot of electrical spring and other contacts used in a typical detector design such as battery contacts, marginal/cold solder connections, chip sockets, cable connectors etc. Metal contracts when cold as will any electrical contact used in the design.
As a rule of thumb, the more electrical contacts are used in a product's design, the less the reliability of that product.