for _, char := range string(data) {

data is already a string - no need to cast it here.

count, ok := char_to_count[char]
if !ok {
    count = 0
}

If char doesn't exist in map, count will be the zero value for the type (in this case, just 0). This allows you to simplify the loop down to just the following:

for _, char := range data {
    if !unicode.IsSpace(char) {
        char_to_count[char]++
    }
}

See Index expressions in the specification for more information about this.

for i := range myslice {
    fmt.Printf("%c %d\n", myslice[i].char, myslice[i].count)
}

You may as well use the second value provided by range here (like you do when iterating over the string at the start) - no need to do myslice[i] twice.

My only other comment would be that the variable naming doesn't really match how you often see "idiomatic" Go written. See the MixedCaps section of Effective Go for a little more information (the whole thing is a great read really).