The usual way to express this is below freezing, which clearly indicates a lower temperature than freezing.
The British National Corpus has 38 results for "below freezing," and none for "more than freezing" or "less than freezing." The Corpus of Contemporary American English has 256 results for "below freezing," and none for "more than freezing" or "less than freezing."
As you say, the temperature is "lower than zero" (if you're using degrees Celsius). We can also speak of temperatures "under zero degrees."
All of the above mainly refers to literal uses of the word "freezing." If you're using it non-literally to mean "very cold," I might prefer to say "colder than freezing," as you do in your title. Note that we would say "colder" than freezing (not "less cold"); this is probably why your brother feels like using "more." However, if your brother just says it is "more than freezing," he may be misunderstood.
How people actually use "more than freezing"
The one example of this phrase I found in the Google Books corpus refers to a temperature above freezing:
Damn, it's hardly more than freezing and I'm sweating like a stuck pig
(Shermans [sic] Creek: A Redneck Murder Mystery, by Ronald A. Hopkins)
And I found another example using Google search where it is used to mean "above 0 °C":
the NWS forecasts that Boone would warm to a little more than freezing
on Monday, while temperatures will drop back below freezing across the
region by midnight tonight.
("Winter Weather Advisory Issued for Tuesday, Warns Commuters of Freezing Rain, Snow, More Rain," by Jesse Wood, HCPress.com)
However, I did also find some people who used it like your brother:
MINUS TEN DEGREES CELSIUS (or -14 F).
That is not “cold.” That is freezing. Actually, that is more than
("TOL: I Literally Almost Froze This Morning," Postcards From the Present)
When we got up this morning it was still -4C outside – and this was at
("Day 364: More than Freezing," by Kathryn Dawson)
Q: It is -22 degrees Celsius in Winnipeg, more than FREEZING ( a
fact), where is global warming? (question listed on experts123.com)
For this reason, I'd say "more than freezing" is not only unusual wording; it is also ambiguous.
How people actually use "less than freezing"
In most cases, "less than freezing" seems to be used the way you'd think it would be used: to refer to colder temperatures than the freezing point of water. Examples:
However, I found one interesting example on Google Books where it seems to be used to mean the opposite, although I'm not entirely sure:
Snow and powdered ice that have ever been ſubjected to a cold leſs
than freezing are ſpoiled, or rendered much leſs fit for experiments
of this kind.
(A Journal of Natural Philosophy, Chemistry and the Arts, Volume 1, by William Nicholson)