C172 Pilot reported carburetor icing during flight. The Pilot took immediate action and turned on carburetor heat; the icing problem dissipated and the Pilot continued the flight to destination airport.

Narrative

I was on a solo cross country flight in VFR conditions en route from ZZZ to ZZZ1. VFR conditions prevailed except for high winds (210 @ 15-19). There was a light haze and no ceiling along the entire route. The purpose of the flight was time building; and to have dinner with a friend in ZZZ1. I did not file a VFR flight plan; opting for VFR flight following. The surface winds at ZZZ initially gave me pause; but I calculated my crosswind component and conducted a crosswind takeoff procedure on Runway XX without incident. I was vectored south of ZZZ2 to avoid commercial traffic landing south; and then resumed own navigation to ZZZ1. The winds aloft were stronger than forecast in my briefing and I burned more fuel than planned due to the strong headwind flying westbound. I would have landed at ZZZ1 with less than 45 minutes of fuel remaining; which violates my personal minimums; so I opted to land at ZZZ3 to quickly refuel and continue on my journey. I took a normal fuel sample after refueling at ZZZ3; and quickly performed my checklists to continue on my journey; as I was already late for dinner in ZZZ1. I was back on course after refueling; cruising at 6;500 Ft. at 2450 RPM; with dusk quickly turning to night. I had leaned the mixture and I had the right wing fuel tank selected. I had deviated slightly north to avoid the active restricted area (artillery) and to stay under [the restricted area] on the approach into ZZZ1. I was approximately 5 miles west of ZZZ4. Suddenly and without warning the engine began to run very rough; followed by a loss of power all the way back to between 12-1300 RPM. My first real immediate situation as a pilot; but my training quickly kicked in. Aviate; I stabilized the aircraft in a low power glide. Navigate; I used the GPS and ForeFlight on my iPad to determine that ZZZ4 was the nearest airport and directly behind me. I turned the airplane to begin setting up for a precautionary landing into ZZZ4. Communicate; I requested priority handling with Center. Center quickly confirmed that ZZZ4 was my nearest and best available airport. I had the airport in sight; and more than enough altitude to make the runway. At this point I had several thoughts: 1. This is really happening. 2. I can make the airport; I am going to be ok; the engine is still running; do not panic. 3. Is there something wrong with the fuel I just put in the airplane? There was nothing wrong with the sample I took. 4. How am I getting home now? My dog is unattended and I have to be at work in the morning. Checklist and Troubleshooting; I had a paper checklist available; but it was folded up; so I opted for memory items instead. Mixture rich; fuel selector both; move the throttle; carburetor heat out. When I applied carburetor heat; the engine RPM initially dropped further; but then spontaneously went back to full power. This is when I realized that I was encountering an extreme case of carburetor icing. With ZZZ4 still an option; I tested and was satisfied with the responsiveness of the throttle. With power restored; I decided that my situation no longer existed; aborted my precautionary landing; and continued to my destination; albeit slightly rattled by the event. I returned the aircraft to ZZZ later that evening without further incident. Aeronautical Decision Making (ADM): ADM that I am satisfied with: Obtaining a weather briefing in ForeFlight prior to the flight. Multiple and accurate crosswind component calculations before a crosswind takeoff. Flying with a ForeFlight Sentry ADS-B receiver to enhance situational awareness. Obtaining VFR flight following on every flight. Verifying the maintenance status of the rental aircraft that I was flying. Conducting a good pre-flight inspection and following checklists. Ensuring the aircraft is full fuel and oil before leaving on a long flight. Flying at high VFR altitudes to allow for better options in a priority situation. Calling minimum fuel and refueling at ZZZ3 rather than risking afuel priority by continuing to ZZZ1 in a strong headwind. Verifying that my flight path would not violate the restricted areas around ZZZ1. Completing a deferred discrepancy report for the aircraft to be inspected by a licensed mechanic following this event. ADM that I can improve: Failure to recognize that conditions were favorable for carburetor icing. Failure to take steps to prevent carburetor icing; such as monitoring the carburetor temperature gauge and applying small amounts of carburetor heat as needed. The majority of my flight training occurred in fuel-injected aircraft where carburetor icing is not an issue. Do not be complacent. The decision to abort a precautionary landing and continue to my destination. Developing the opinion that the aircraft was airworthy again once the aircraft was operating normally and the situation condition ceased to exist. Reluctance to delay or cancel flightsExternal Factors and Pressures: Wanting to be on time for dinner in ZZZ1. Wanting to impress the friend that I was flying to ZZZ1 to meet. Needing the flight time for my next airman certificate. Needing to return to my origin in a timely manner so that my dog would not be left unattended for an unreasonable amount of time. Needing to return to my origin in a timely manner so that I would be on time for work the next morning. Having to pay and be reimbursed for any aircraft expenses incurred while it is away from the home airport ('wet rental'). Being responsible for transportation back to the origin should the aircraft become unairworthy away from the home airport. Someone had the aircraft reserved after me. In the end; I get to learn a valuable lesson from this experience and apply that knowledge to be a better pilot. This report would be incomplete if I did not compliment the professionalism of the air traffic controllers at Center; Approach; and ZZZ1 Tower for contributing to the positive outcome of this experience.