If you were to put an animal with a certain type of seemingly advantageous "trait" into an environment where the trait was not necessarily needed, ex: Putting an animal with a high tolerance for cold into a mild climate, what kind of natural selection occur? Balancing?
Recipe for selection
There is selection on a specific phenotypic trait if and only if
- There is variance for this trait in the population
- This variance is, in part at least, explained by genetic variance
- The trait covaries with fitness
The first two points can be reduced to a single point by stating "The trait has some non-zero heritability in the population". For more information about heritability, please have a look at Why is a heritability coefficient not an index of how “genetic” something is?.
This recipe is often called Lewontin recipe.
Applying the recipe to your case
So, in the model you consider, some individuals are cold tolerant and some aren't, so the first point is checked!
We will assume that the difference in cold tolerance is caused by genetic differences. Second point is checked.
Does the trait covary with fitness? As you defined that, in the environment considered, being cold tolerant does not have any impact on fitness, then no, there is no covariance between the trait and fitness. The third point is not checked and therefore, there is no selection happening.
Are you sure there is no cost to being cold tolerant?
Note, btw, that it is not rare to observe (or at least to assume) that some adaptation such as cold tolerance would come at a comparable cost when the environment is warm enough.
For example, increased cold tolerance might be mediated via anti-freeze proteins. The production of such proteins might be costly for the individual. In such case, we would have a covariance between fitness and the trait (cold tolerant individuals would have lower fitness that individuals that are not cold tolerant) and hence selection should act as to reduce the frequency of individuals that are cold tolerant in the population (always assuming an environment that is warm).
What else could cause the frequency of cold tolerance to evolve?
In absence of selection, the frequency of cold tolerance individuals might still evolve in the population. Things like genetic drift, selection at linked site or selection at correlated trait or migration can typically affect this frequency.