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I can see why you think this way but I would imagine that this is quite a risky choice for this crime. It is very close (just a few walking minutes) to dense residential population with footpaths and dog walking routes, busy thoroughfares and cycling routes.
My experience in lockdown was that the world and his wife was out walking dogs, jogging, cycling, strolling with mates, teenagers seeking outdoor adventures - just to grab some fresh air and a change of scene. I live in an area where we are just villages spread through our surrounding area and finding space to yourself, where you previously were used to finding it, was nigh on impossible! Particularly at midday on a Saturday afternoon in July. Even if he was lucky to stay invisible in the few minutes an actual murder may have taken, there would have been a struggle, screaming, and then attempting to conceal a body where a dog, or a person might discover it; in this potentially busy location, at this peak time, would be very risky indeed.
I am not familiar with the area just a few minutes further out of the city towards the fens, but I would imagine the further you go the less risk there is.
Horses can be found anywhere if you are looking for them and you have a car at your disposal, if you feel this is key ‘slippage’.