The clicky noise is likely to be the starter solenoid. The fact it makes a clicky noise is likely a good thing - the starter is working but it isn't turning the engine over. If you've been attempting to start the thing repeatedly it is likely that the battery isn't DEAD dead but does not have enough left to start the bike.
It sounds to me like the engine is simply very very cold. Have you previously been fine starting it on cold mornings? Have you actually started it on choke before? My bike doesn't like starting on choke at all - I solve this by, when I start it, revving the throttle and holding it open up to the revs it usually pulls while it's on choke. If the revs stay constant whilst holding the throttle open like this then put the choke on gently. If they drop off then be patient and keep it constant; if it dies try it again but don't be so hard revving it as you start it.
With some bikes, starting them in cold weather really is an art form.
Have you tried bump-starting it? Have you tried jumping it? (note: careful jumping off cars, never let them start their engine while your bike is connected, just start it off their cold battery - you can damage a bike's battery jumping off cars if you're not careful).
Don't go faffing with spark plugs if you don't know what you're doing. If it was running fine yesterday they're probably alright.