I am not clear exactly what you are wanting to test here. Do you have a hypothesis? You can certainly take a sampling approach in evaluating the "accuracy" of the lower resolution binominal classification along with hypothesis testing the distributional equivalence of the binominal classes.

Here is a worked example, in R, of what testing a hypothesis and evaluating accuracy would look like. The example is provided in R because ArcGIS just does not have the tools to perform this type of analysis.

First, let's add our required libraries and create some example data. Please note that the higher resolution raster contains random values on a proportional scale and the lower resolution data is binominal thus, emulating your problem. The results in the example cannot be interpreted literally due to the binominal data being a thresholded function of the higher resolution proportional data but, it gives the analytical framework for real data.

library(raster)
library(sp)
library(rfUtilities)

r.high <- raster(nrows=180, ncols=360, xmn=571823.6, xmx=616763.6, ymn=4423540, 
            ymx=4453690, resolution=100, crs = CRS("+proj=utm +zone=12 +datum=NAD83 
            +units=m +no_defs +ellps=GRS80 +towgs84=0,0,0"))
    r.high[] <- runif(ncell(r.high),0,1)
r.low <- aggregate(r, fact=6, fun=median)
  r.low <- reclassify(r.low, matrix(c(0,0.5,0,0.5001,1,1), 
                      ncol=3, byrow=TRUE))

par(mfrow=c(1,2))
  plot(r.high)
  plot(r.low)

Now that we have a reproducible example we can create a random sample, across the higher resolution raster (which will contain the associated cell values) and then extract the values for the low-resolution data.

rs <- sampleRandom(r.high, 5000, sp=TRUE)
  rs@data <- data.frame(rs@data, extract(r.low, rs))
    names(rs) <- c("high_res", "low_res")

For hypothesis testing, using the Kruskal-Wallis Test, we can decide whether the population distributions are identical without assuming a normal distribution. The null hypothesis is that the snow proportions in the higher resolution data are identical populations across the binominal [0,1] values.

kruskal.test(rs$high_res ~ rs$low_res, data = rs) 

We can also use the log loss statistic to evaluate the accuracy, of the low-resolution data, based on penalizing the magnitude of the "miss-classification". Make sure that, if you are dealing with percentages, that you rescale to a 0-1.

logLoss(y=rs$low_res, p=rs$high_res)

We can also evaluate the data by splitting out the two classes. The Kolmogorov-Smirnov test evaluates the distributional equivalence and Mann-Whitney is a nonparametric test where the null hypothesis is that for randomly selected values x and y from two populations, the probability of x being greater than y is equal to the probability of y being greater than x.

ks.test(rs@data$high_res[which(rs$low_res == 1)], 
        rs@data$high_res[which(rs$low_res == 0)])
wilcox.test(rs@data$high_res[which(rs$low_res == 1)], 
            rs@data$high_res[which(rs$low_res == 0)], 
            alternative = "g")

You can also plot the distribution of the two classes.

one.pdf <- density(rs@data$high_res[which(rs$low_res == 1)])
zero.pdf <- density(rs@data$high_res[which(rs$low_res == 0)])
  par(mfrow=c(2,1)) 
     par(mar=c(0,5,3,3))
       plot(one.pdf, type="n", main="Distribution of proportions by class", 
        xlim=range(0,1), ylim=range(one.pdf$y),
        xlab="Class one",
        ylab="", xaxt="n", las=1)
        polygon(one.pdf, col="red")
        abline(v=range(rs$high_res), lty=3, lwd=1.5)
     par(mar=c(5,5,0,3))
       plot(zero.pdf, type="n", main="", 
           xlim=range(0,1), ylim=rev(range(zero.pdf$y)),
           xlab="Class zero",
           ylab="", las=1)
        polygon(zero.pdf, col="blue")
        abline(v=range(rs$low_res), lty=3, lwd=1.5)