According to the official google website. 
Not all watches have a Wi-Fi feature. Try using the directions below to connect to Wi-Fi. If you don’t see Wi-Fi settings under “Settings” on your watch, Wi-Fi is not available on your watch.
When your watch uses Wi-Fi, the “Open on phone” feature is disabled.
Your watch can’t connect to Wi-Fi networks that use captive portals, which are web pages you have to visit before connecting.
You will need to download tools to be able to connect to your watch.
1. [TOOL] [WINDOWS] ADB, Fastboot and Drivers - 15 seconds ADB Installer v1.4.2
Your watch needs to have USB debugging enabled. Follow this youtube guide. Since UI is the same on all android wear, this method will work on all android wear watches. Note that the person in the video has a Mac. So the console will be different. On windows you just fire up the cmd. You can ignore the Android SDK and Eclipse stuff she is doing as we don't need it for this.
This tool has a list of supported devices, but since we are going to be using only one function of it, you can probably get away with picking the wrong android wear watch from the list.
3. Download [TOOL] WinDroid Universal Android Toolkit v2.4 | Unlock | Root | Flash | 90+ Devices
From previous steps make sure your watch is connected and the WinDroid tool is able to detect it. If all is good download APKs and then in WinDroid go to "Commands" tab and click on "Install App". Find your firefox and minuum wear apk files. Install both of them by installing one at a time.
Once apks are installed you need to open cmd terminal and type some commands:
To make keyboard work you need to type
adb shell ime enable com.whirlscape.minuum/.MinuumKeyboardService
adb shell ime set com.whirlscape.minuum/.MinuumKeyboardService
To make firefox UI more usable, we need to change the LCD density.
In the same terminal first type
cat /system/build.prop | grep "lcd"
To change density type
wm density 200
Now try connecting to the public wifi on your smartphone. Wait a few seconds for information to sync with your watch. Disable bluetooth on your phone and your watch should automatically try to connect to wifi hotspot. Alternatively you can select wifi AP from a list of wifi on your watch without needing to use your phone. You will still need to disable bluetooth on your phone though.
Finally, fire up firefox on your watch, try to go to any website. The captivity webpage of your public wifi will show up and just press accept/I agree/etc as you normally would. After that you can close firefox by swiping to the right. I recommend you install task manager for android wear to be able kill firefox from memory. And try not to leave firefox or wifi open for too long as it will drain your battery really quick.
Now sit back and enjoy your wifi sync over the public wifi hotspot connection.
This lets your watch and phone to automatically stay synced at any distance over the Internet.
Here how it all looks on my watch.
Sadly video doesn't start, it just keeps on buffering.