Mobile device detection via htaccess: Cookie isn't set on first "try" - .htaccess

Question

Based on what was written here, I was able to set up a mobile device detection using htaccess. I added the functionality to be redirected back to the desktop site from m.example.com in case the user does not visit the site with a mobile device. Additionally I added an environment variable to preserve http/https requests:
# Set an environment variable for http/https.
RewriteCond %{HTTPS} =on
RewriteRule ^(.*)$ - [env=ps:https]
RewriteCond %{HTTPS} !=on
RewriteRule ^(.*)$ - [env=ps:http]
# Check if m=1 is set and set cookie 'm' equal to 1.
RewriteCond %{QUERY_STRING} (^|&)m=1(&|$)
RewriteRule ^ - [CO=m:1:example.com]
# Check if m=0 is set and set cookie 'm' equal to 0.
RewriteCond %{QUERY_STRING} (^|&)m=0(&|$)
RewriteRule ^ - [CO=m:0:example.com]
# Cookie can't be set and read in the same request so check.
RewriteCond %{QUERY_STRING} (^|&)m=0(&|$)
RewriteRule ^ - [S=1]
# Check if this looks like a mobile device.
RewriteCond %{HTTP:x-wap-profile} !^$ [OR]
RewriteCond %{HTTP_USER_AGENT} "android|blackberry|ipad|iphone|ipod|iemobile|opera mobile|palmos|webos|googlebot-mobile" [NC,OR]
RewriteCond %{HTTP:Profile} !^$
# Check if we're not already on the mobile site.
RewriteCond %{HTTP_HOST} !^m\.
# Check if cookie is not set to force desktop site.
RewriteCond %{HTTP_COOKIE} !^.*m=0.*$ [NC]
# Now redirect to the mobile site preserving http or https.
RewriteRule ^ %{ENV:ps}://m.example.com%{REQUEST_URI} [R,L]
# Check if this looks like a desktop device.
RewriteCond %{HTTP_USER_AGENT} "!(android|blackberry|ipad|iphone|ipod|iemobile|opera mobile|palmos|webos|googlebot-mobile)" [NC]
# Check if we're on the mobile site.
RewriteCond %{HTTP_HOST} ^m\.
# Check if cookie is not set to force mobile site.
RewriteCond %{HTTP_COOKIE} !^.*m=1.*$ [NC]
# Now redirect to the mobile site preserving http or https.
RewriteRule ^ %{ENV:ps}://example.com%{REQUEST_URI} [R,L]
This works fine except one thing: When I visit m.example.com/?m=1 from a desktop device, I'm redirected to example.com although I should "stay" on m.example.com. When I try again, I "stay" at m.example.com. It seems as if the cookie isn't set and/or read correctly the first time.
Any ideas what could be the problem?