Unless you have evidence in the text that only deer ran about there, perhaps a more general term would be safer. I'll post some references in in a moment.

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Note added at 21 mins (2008-09-30 19:21:35 GMT)
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"Kiveton was once the site of a stately home - Keeton Hall, home of the 1st Duke of Leeds, now in a family vault in Harthill church. Most of the area was part of the Dukes hunting park; hence the full title of Kiveton Park. The Hall was demolished in 1812 with only the stables remaining, which form part of the present day Kiveton Hall Farm (on the road between Kiveton and Todwick)."
( From: http://tinyurl.com/3kk99s )

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Note added at 23 mins (2008-09-30 19:23:20 GMT)
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"The Park Tunnel was built in 1855 to allow horsedrawn carriages access to the Park from Derby Road in Nottingham. This area was formerly a private hunting park for the Duke of Newcastle who was also the owner of Nottingham Castle Mansion."
( From: http://tinyurl.com/47baz7 )

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Note added at 25 mins (2008-09-30 19:25:35 GMT)
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"The priory is situated in Hulne Park, a walled park covering several thousand acres which belongs to the Duke of Northumberland and is close to Alnwick Castle. Originally a hunting park, and still used by the Duke for shooting (...)"
( From: http://tinyurl.com/4dxnyg )

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Note added at 29 mins (2008-09-30 19:29:52 GMT)
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"During the two millenia in which parks have been carved out of the English countryside, and latterly inserted into English towns, they have taken different forms, reflecting different social and economic criteria. First introduced by the Normans, they were originally hunting parks devised to contain deer for their lordly owners to hunt."
( From: http://tinyurl.com/5ysy4z )

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Note added at 3 hrs (2008-09-30 22:06:17 GMT) Post-grading
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I'm glad to have been able to help. But forgive me if I suggest that it really is a good idea to leave questions open for 24 hours, as the KudoZ rules recommend:

http://www.proz.com/siterules/kudoz_asking/2.11#2.11

since it gives people who may not be online at the moment of asking or who are in other time zones the chance to answer and something more appropriate to your text might well come up in that way.

Good luck!