Yes, a reflective meter will give the exposure to get middle gray. This is great with a spot meter, allowing us to use the Zone System, but there's shortcomings when it's an averaging matrix :
Simple experiment to do with a digital camera in center-weighted metering mode or simply your phone camera : point it at a scene in bright daylight with equal foreground and sky. Chances are the foreground will be underexposed to protect the highlights (the sky). Move the camera/phone slightly upward (more sky), this will increase the phenomenon further. Move it downward, the exposure on the foreground will be better, and the sky will be brighter, probably overexposed. With digital, we can easily see that in real time and adjust our exposure, and the default computed exposure (foreground underexposed, highlight protected) is actually good. This is because digital sensor have low tolerance in the highlights, but there is a large margin to boost the exposure of underexposed areas in post, especially when shooting raw.
The problem with film camera is that we can't see how the camera metered the scene, and with black and white negative film we want the opposite : give the shadows enough exposure and not worry so much about the highlights because i) moderns general-purpose B&W films can register a ton of informations in the highlights but don't like underexposure very much ii) we'll handle the density of the highlight when developing. This is the famous "expose for the shadows, develop for the highlights". For theses reasons using the camera built-in light meter, while convenient, is the least recommend way of metering : an incident meter or a spot meter are much betters tools*
BUT, if we're stuck with the camera's built-in meter, there's still techniques we can use. I'm going to paraphrase my go-to book, "The Zone system for 35mm photographers" by Carson Graves, pp.32 and 89-91
1) Walking up to a coherent part of the scene until it completely fills the viewfinder, while being careful not to cast our shadow on it : the snow, a patch of green grass ... and take the meter reading. Now we use the Zone System to place that part of the scene where we want to. As an example adding one stop to place the snow in zone VI, or leaving the sun-lit grass in zone V. Basically, it's the same as if we metered the zone from afar using a spot meter.
Of course it's not always possible or practical to do so. An other option is to use our hand as reference :
2) The book is more detailed (taking a reading in light AND shadows, giving an indication of the overall contrast and therefore the N/N+/N-development to use) but a simple way to explain the technique is to place the palm of our hand in a position where it reflects the greatest amount of available light, fill the viewfinder with it (while being careful not to cast shadow on it) and take a meter reading. We assume that the hand in light is zone VI, so as the camera gave the exposure to get Zone V, we add one stop, and that's the exposure for our shots as long as the light remain the same.
*Unfortunately spot meters are ridiculously expensive, even used one. Incident meters are cheaper. I use the Sekonik FlashMate L-308X and it's one the best investment I did.