The Survey of English Dialects (undertaken between 1950 and 1961) lists "morning sticks" as a Shropshire phrase i.e. the county immediately east of Welshpool, Powys. The similar "morning wood" {stop sniggering at the back!} was (is?) used in nearby Herefordshire and Gloucestershire, along with distant Essex and Kent.
Clearview Stoves make mention of their Pioneer Oven having a fuel store, "the perfect place to dry your morning sticks". Suffice to say Clearview Stoves is a Shropshire business.
http://www.clearviewstoves.com/pioneeroven.htm