Well, usually not. Normal rains do not affect GPS reception, but heavy clouds, eventual thick fogs or snow could be a hindrance for the signals to reach GPS receiver, just like you loose signals while watching TV on a heavily clouded day with thunderstorms.  

Let’s consider the case of a GPS tracking device without an inbuilt GPS antenna. To ensure the quality of GPS signals, you got to place this antenna separately somewhere visible, so it’s well exposed to the sky. Chances are less that you fix this antenna on the outer body of the vehicle. If you do so, that’s probably the end of it, even a soaked cloth may put an end to the signal reception, needless to say about rain/snow falling on GPS device/antenna.

In the rarest of the rarest cases, magnetic fields generated by the sun causing solar flares, or emission of intense radio waves from a star (radio burst) may result in reduced GPS signal reception.

However, now you may find numerous GPS tracking devices with inbuilt GPS antenna, manufactured to IP67 (Ingress protection) compliance standards, that denote full resistance to dust and water (immersion level of up to 1m)

Though weather variations cannot be accounted much for weakening signals, geography does play a vital role. Thick forests, underground parking spaces, signal jammed sites etc make GPS signals unconditionally weak, eradicating them from being received on GPS tracking devices.