right. ... now that snow is patchy, but the picture is obviously later in the day. you'd expect the areas that are exposed grass in the image there to have had the light dusting at 6 AM. on top of near-continuous old snow coverage over big swaths of the yard. probably enough to expect to see tracks. at least for the parts of the front yard visible in that picture.
i do also wonder how much the old snow coverage and/or new dusting varied around the house at 6 AM... if i'm not mistaken, that picture you just posted is looking due west. so the far side of the house (from this perspective) doesn't get sun until after noon. the old snow cover on brick/stone surfaces might conceivably have melted on previous afternoons, but the fresh dusting from the night before should still have been there at 6 am.
this is not a complete accounting of all approaches to the house, but i'm getting more convinced the snow cover was such that you'd expect an intruder to leave footprints.
There's another photo of the front yard taken earlier in the day, one with a police cruiser in it - showing more snow - just couldn't locate it right away. You're correct about the orientation of the house
The police were particularly interested in the grassy area around the grate. Even if the snow had already disappeared from the brick/stone surfaces at 6:00 AM, it would still have been on the grass, and that space was big enough to have retained footprints.