Why is taxiing super slow after an ILS CATIIIB landing in almost zero visibility? I have experienced my very first ILS CAT IIIB automatic landing at my own home airport Lucknow (VILK). I'm super excited but also have myriads of questions related to many unique procedures I saw which I never seen in all my years of flying. Even though I was happy to have experienced such a magical landing, I was afraid how are we gonna park now because it was all white and the taxiing on this flight was the literally the slowest taxiing I have ever seen in my life.
After we landed and I could barely see the taxiway markings and even the runway borderline was hard to see. We crawled to the end of the runway to make a 180 degree and backtrack to vacate via taxiway C. The plane had already slowed down on its initial landing roll and at that time I didn't know about any special procedures or anything like low visibility conditions.
I was wondering why we did not exit via Taxiway B or C or even D or E when we had so many chances to do so and why we had to come all the way to the end of the runway only to go back and exit via C again and park at bay 13?
If any pilots here who have flown in CAT IIIB conditions, I wanna know how hard it is to find the taxiways in such a thick fog?
The reason for using taxiway C is described in the Low Visibility Procedures from the AIP:

4.4.4 At present, TWY ‘C’ and Stand no 11 to 14 are equipped with CAT IIIB lighting system as per short term interim plansubmitted to DGCA by AAI and agreed to by DGCA vide letter no. AV.20015/09/08-AL dated 15-07-2014. Therefore, duringCAT IIIA and CAT IIIB operations, arrivals and departures shall use TWY ‘C’ only.

So the reason you had to taxi via C is because C is the only taxiway with sufficient lighting to support CAT III operations. For CAT III operations, taxiway centreline lights are required. The other taxiways at Lucknow only have taxiway edge lights.
Source: https://aim-india.aai.aero/eaip-v2/eAIP/EC-AD-2.1VILK-en-GB.pdf
The reason you had to backtrack (turn around on the runway and taxi back in the opposite direction) must be that the plane was not slow enough to vacate via C when you passed it the first time. I know you said you had already slowed down, but in thick fog it can be pretty hard to estimate speed, especially when looking out a side window. The pilots obviously have access to precise instruments, and must have determined that the aircraft had not slowed down enough.