A member has posted a notice “Buckthorn Herbicide and White Oak” to the Notice Board. If you might be able to assist, log in to the BGWA Notice Board to read/respond.
NEW Members’ Notice Board Posting
Bruce Grey Woodlands Association
Promoting healthy forests and ecosystems in Bruce and Grey Counties through education, recreation and sustainable management practices.
Bruce Grey Woodlands Association 
https://treescanadensis.ca/quercus-alba-white-oak/
This link carefully documents that white oak grows in the Ottawa area.
One would expect that the Owen Sound area is less harsh temperature wise due to the ameliorating effect of the lakes.
There are many factors related to how quickly plants moved north after the last ice age. Temperature is just one of them. The lakes themselves might form a barrier for example. Squirrels might not be good swimmers.
If one was concerned they could get white oak acorns from the Ottawa area rather than from further south. See distribution map.
http://powo.science.kew.org/taxon/urn:lsid:ipni.org:names:295763-1