There were absolutely no Tiger tanks that were part of the 6th Army or part of the battle for the city of Stalingrad itself or trapped in the Kessel. However, there is conflicting information about what role if any Tiger tanks played in Manstein's relief effort, Operation Winter Storm. We know for sure that Hitler dispatched the first full battalion of Tiger Tanks to participate in the battle, what we do not know is whether they made it there in time to actually take part in Winter Storm. Most records, which are just that, records of times and dates, show them arriving too late and not fighting until early January in an effort to keep the Rostov escape route open to Army Group Don.
However, Antony Beevor in his book Stalingrad, seems to believe that Tiger Tanks were involved in Winter Storm. He mentions them twice in his book.
The first is:
"[Hitler] was impatient to discover how the new Tiger tank, with its 88mm gun, would perform. The very first battalion to be formed had been rushed to the Ostfront and added to Kirchner's force [LVII Panzer Corps]"
This is certainly evidence that the intent was there, however, it does not conclude one way or another if they actually took part.
However, he then goes on to say of Winter Storm itself:
"On the second day of the offensive, 6th Panzer Division reached the Verkhne-Kumsky....On the high ground round this village began what General Raus [6th Panzer Division] describedas a 'gigantic wrestling match'....It proved a success locally - Hoth's divisions and the Tiger tanks advanced to the line of Myshkova, once 17th Panzer Division arrived and Richtofen threw in maximum air support."
This is pretty anecdotal evidence at best, but it's clear that Beevor believed they took part when he wrote this. He could very well be mistaken as there has been some confusion about the fact that the Tigers apparently fought with 17th division after Winter Storm. I really don't know. I would think if they did take part in Winter Storm at least someone would have mentioned it in their memoirs, such as Manstein or Raus, so I wonder where Beevor got his information. He quotes Raus in this same passage.
Either way, Tiger tanks undisputedly took part in the overall Stalingrad campaign in the swirling actions outside the kessel if not as part of Winter Storm, then in the defense against Soviet Operation Little Saturn. So we could make a "winter tiger" for our Stalingrad range and not be out in left field. However, this doesn't mean we're going to do so as there are plenty of other wonderful vehicles to make that were part of the direct battles in the city and would compliment our range quite nicely.
Best,
Matt