Output first:

$ ./1.icons.pl 
{
  "\@context" => [],
  "icons" => {
    bkn             => { description => "Mostly cloudy" },
    blizzard        => { description => "Blizzard" },
    cold            => { description => "Cold" },
    dust            => { description => "Dust" },
    few             => { description => "A few clouds" },
    fog             => { description => "Fog/mist" },
    fzra            => { description => "Freezing rain" },
    haze            => { description => "Haze" },
    hot             => { description => "Hot" },
    hurricane       => { description => "Hurricane conditions" },
    ovc             => { description => "Overcast" },
    rain            => { description => "Rain" },
    rain_fzra       => { description => "Rain/freezing rain" },
    rain_showers    => { description => "Rain showers (high cloud cove
+r)" },
    rain_showers_hi => { description => "Rain showers (low cloud cover
+)" },
    rain_sleet      => { description => "Rain/sleet" },
    rain_snow       => { description => "Rain/snow" },
    sct             => { description => "Partly cloudy" },
    skc             => { description => "Fair/clear" },
    sleet           => { description => "Sleet" },
    smoke           => { description => "Smoke" },
    snow            => { description => "Snow" },
    snow_fzra       => { description => "Freezing rain/snow" },
    snow_sleet      => { description => "Rain/sleet" },
    tornado         => { description => "Tornado" },
    tropical_storm  => { description => "Tropical storm conditions" },
    tsra            => { description => "Thunderstorm (high cloud cove
+r)" },
    tsra_hi         => { description => "Thunderstorm (low cloud cover
+)" },
    tsra_sct        => { description => "Thunderstorm (medium cloud co
+ver)" },
    wind_bkn        => { description => "Mostly cloudy and windy" },
    wind_few        => { description => "A few clouds and windy" },
    wind_ovc        => { description => "Overcast and windy" },
    wind_sct        => { description => "Partly cloudy and windy" },
    wind_skc        => { description => "Fair/clear and windy" },
  },
}
URL = https://api.weather.gov/icons/land/day/tsra_sct,20/tsra_sct,40?s
+ize=medium
   tsra_sct => 'Thunderstorm (medium cloud cover)'

URL = https://api.weather.gov/icons/land/day/rain_showers,30/tsra_hi,3
+0?size=medium
   tsra_hi => 'Thunderstorm (low cloud cover)'

URL = https://api.weather.gov/icons/land/night/rain_showers,30/rain_sh
+owers?size=medium
   rain_showers => 'Rain showers (high cloud cover)'

URL = https://api.weather.gov/icons/land/day/bkn?size=medium
   bkn => 'Mostly cloudy'

$
[download]

The following is essentially a hybrid of Marshall's script with the sausages that come from curl2lwp converter. Source:

#!/usr/bin/perl -w

use strict;
use LWP::UserAgent;
use Data::Dump;
use JSON::Parse 'parse_json';

my $ua = LWP::UserAgent->new( 'send_te' => '0' );
my $r  = HTTP::Request->new(
  'GET' => 'https://api.weather.gov/icons',
  [
    'Cache-Control' => 'max-age=0',
    'Connection'    => 'keep-alive',
    'Accept' =>
'text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,*/*;
+q=0.8',
    'Accept-Encoding' => 'gzip, x-gzip, deflate, x-bzip2, bzip2',
    'Accept-Language' => 'en-US,en;q=0.5',
    'Host'            => 'api.weather.gov:443',
    'User-Agent' =>
'Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:74.0) Gecko/20100101 Firef
+ox/74.0',
    'Upgrade-Insecure-Requests' => '1',
  ],

);

my $out;
my $res = $ua->request( $r, );
if ( $res->is_success ) {
  my $json = $res->decoded_content;
  $out = parse_json $json;
}
else {
  print "Error: " . $res->status_line . "\n";
}

dd $out;

my %xlated_abbrev;    #simple abbreviation table => description

foreach my $key ( keys %{ $out->{icons} } )    #gen simple xlate table
{
  $xlated_abbrev{$key} = $out->{icons}{$key}{description};
}

my @urls = (
  'https://api.weather.gov/icons/land/day/tsra_sct,20/tsra_sct,40?size
+=medium',
  'https://api.weather.gov/icons/land/day/rain_showers,30/tsra_hi,30?s
+ize=medium',
  'https://api.weather.gov/icons/land/night/rain_showers,30/rain_showe
+rs?size=medium',
  'https://api.weather.gov/icons/land/day/bkn?size=medium'
);

foreach my $url (@urls) {
  my $last_path = ( split( '/', $url ) )[-1];
  my ($abbrev_to_xlate) = $last_path =~ /^(\w+)/;

  print "URL = $url\n";
  print "   $abbrev_to_xlate => \'$xlated_abbrev{$abbrev_to_xlate}\'\n
+\n";
}

__END__

Created from curl command line
curl 'https://api.weather.gov/icons' -H 'User-Agent: Mozilla/5.0 (X11;
+ Ubuntu; Linux x86_64; rv:74.0) Gecko/20100101 Firefox/74.0' -H 'Acce
+pt: text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,
+*/*;q=0.8' -H 'Accept-Language: en-US,en;q=0.5' --compressed -H 'Conn
+ection: keep-alive' -H 'Upgrade-Insecure-Requests: 1' -H 'Cache-Contr
+ol: max-age=0'
[download]

The script I used to make png's of the icons follows:

#!/usr/bin/perl

use strict;
use warnings;
use Log::Log4perl qw(:easy);
use WWW::Mechanize::Chrome;

my $a = 'b';

my @urls = (
  'https://api.weather.gov/icons/land/day/tsra_sct,20/tsra_sct,40?size
+=medium',
  'https://api.weather.gov/icons/land/day/rain_showers,30/tsra_hi,30?s
+ize=medium',
  'https://api.weather.gov/icons/land/night/rain_showers,30/rain_showe
+rs?size=medium',
  'https://api.weather.gov/icons/land/day/bkn?size=medium'
);

foreach my $url (@urls) {

  show_screen( $a, $url );
  $a++;

}

sub show_screen() {
  my ( $letter, $url ) = @_;
  my $mech = WWW::Mechanize::Chrome->new();
  $mech->get($url);
  my $page_png = $mech->content_as_png();
  my $base     = '/home/hogan/5.scripts/1.corion./template_stuff/aimag
+es';
  my $fn       = $base . "/$letter.png";
  open my $fh, '>', $fn
    or die "Couldn't create '$fn': $!";
  binmode $fh, ':raw';
  print $fh $page_png;
  close $fh;
  print "exiting show_screen with letter $letter\n";

}

sleep 1;
[download]

I didn't really understand any of this until I could see what the icons actually look like:

For example, on the left side of this icon, chance of rain is 20%, and on the right, 40%.