Append a list as a column in a dataset

One way:

ds // Transpose // Append["intervals" -> intervals] // Transpose

In Mathematica it is usually easier to operate on rows, which is what this solution demonstrates. I would have done the same if I was working with lists too. However, as other answers show there are dataset specific solutions that might work better.

Another way:

ds[MapThread[Append[#1, "intervals" -> #2] &, {#, intervals}] &]

Suppose your column is a list of Association objects or a Dataset:

ds = Dataset[{
<|"char" -> 1, "freq" -> 0.1|>,
<|"char" -> 2, "freq" -> 0.2|>,
<|"char" -> 3, "freq" -> 0.3|>,
<|"char" -> 0, "freq" -> 0.4|>
}];

intervals = {{0, 0.4}, {0.4, 0.7}, {0.7, 0.9}, {0.9, 1.}};

assoc=<|"interval"->#|>& /@ intervals;
col = Dataset[assoc];

Then you can simply use Join to add a column:

Join[ds, assoc, 2]
Join[ds, col, 2]