Unless you made a Late Check-in you will be late. You are leaving on a 3+ hour flight and when you add in the time zone +1 you will not arrive at MIA until after 7 PM. I think check-in times are usually around 1-4PM, so you best make sure you have a late check-in arranged.
Now as for the snow, that will have little difference on your flight. BUT you must remember the airline is not keeping a 100 million dollar airplane sitting on the ramp in ORD for you. That airplane will have been flying since 5, 6 or 7 AM that morning. Where does it fly to/from? Well you will need to contact Operations Control and trust me you can't find the number (they wouldn't tell you anyway and probably notify Homeland Security if you got the number.)
Whether you will be delayed depends on where the plane is coming from. Was it delayed earlier by a blizzard in Minor North Dakota? Did it have a mechanical problem in San Juan PR? Was there an overbooking problem in Boston or San Francisco? This and a hundred things you could not think of are what cause delays.
your only option is to be at the counter ON TIME. If there are problems on the Kennedy then that should be a bigger concern for you. What about parking and how about security lines? Also remember it is still the holiday travel season - bigger lines, bigger problems, bigger everything!
Just use these basic numbers and you will be fine.
1. Be at the gate no later than 30 minutes prior to departure. I know it says 15 but if the flight is over booked (and it could be especially if an earlier flight were cancelled and they are putting people on YOUR flight) this is when they start to kick people off. You come at 15 minutes before you could wind up spending the night in ORD.
2. Be at the ticket counter 90 minutes prior to departure. I know they say 45 minutes for domestic and 90 minuter for international (2:30 for international with me), but once again at the ticket counter is not at the gate. Just because you check in at the TC does not mean you will get on the flight. That is because of TSA and all the garbage.
3. Pass through all security checkpoints at least 40 minutes prior to departure. This will give you time in case of hickups.
4. Once at the gate (unless you go to a business class longe for THAT AIRLINE) do not get out of listening range of the gate. Many people have checked in and gone to the bar or restaurant and missed their flight because it left EARLY. They do leave early when we as pilots have problems like gate holds, flow control or slot times. I am not going to get into those but I have gone to the agent and said, "if we don't leave in the next 5 minutes we will have a 3 hour gate hold."
The agents close out the flight early and I personally have departed 15 minutes early.
Good luck