ref : http://www.baku-dreameater.net/archives/8741 and revised. Article -> http://tech.guitarrapc.com/entry/2016/01/24/032718

WeatherHacks.cs

void Main()
{
    //東京都のID
    var cityCode = "130010";
    WeatherHacks.GetWeather(cityCode).Result.Dump();
}

public class WeatherHacks
{
    private const string baseUrl = "http://weather.livedoor.com/forecast/webservice/json/v1";

    public static async Task<WeatherResponse[]> GetWeather(string cityCode)
    {
        var url = $"{baseUrl}?city={cityCode}";
        var result = await new HttpClient().GetAsync(url, HttpCompletionOption.ResponseHeadersRead);
        var jsonString = await result.Content.ReadAsStringAsync();
        var json = JObject.Parse(jsonString.ToString());
        var response = json["forecasts"].Select(x => new WeatherResponse {Date = DateTime.ParseExact(x["date"].ToString(), "yyyy-MM-dd", null), Telop = x["telop"].ToString()}).ToArray();
        return response;
    }
}

public class WeatherResponse
{
    public DateTime Date { get; set; }
    public string Telop { get; set; }
}

WeatherHacksClass.cs

void Main()
{
    //東京都のID
    var cityCode = "130010";
    WeatherHacksClass.GetWeather(cityCode).Result.Dump();
}

public class WeatherHacksClass
{
    private const string baseUrl = "http://weather.livedoor.com/forecast/webservice/json/v1";

    public static async Task<WeatherResponse> GetWeather(string cityCode)
    {
        var url = $"{baseUrl}?city={cityCode}";
        var result = await new HttpClient().GetAsync(url, HttpCompletionOption.ResponseHeadersRead);
        var jsonString = await result.Content.ReadAsStringAsync();
        var response = JsonConvert.DeserializeObject<WeatherResponse>(jsonString);
        return response;
    }
}

public class WeatherResponse
{
    public Pinpointlocation[] pinpointLocations { get; set; }
    public string link { get; set; }
    public Forecast[] forecasts { get; set; }
    public Location location { get; set; }
    public DateTime publicTime { get; set; }
    public Copyright copyright { get; set; }
    public string title { get; set; }
    public Description description { get; set; }
}

public class Location
{
    public string city { get; set; }
    public string area { get; set; }
    public string prefecture { get; set; }
}

public class Copyright
{
    public Provider[] provider { get; set; }
    public string link { get; set; }
    public string title { get; set; }
    public Image image { get; set; }
}

public class Image
{
    public int width { get; set; }
    public string link { get; set; }
    public string url { get; set; }
    public string title { get; set; }
    public int height { get; set; }
}

public class Provider
{
    public string link { get; set; }
    public string name { get; set; }
}

public class Description
{
    public string text { get; set; }
    public DateTime publicTime { get; set; }
}

public class Pinpointlocation
{
    public string link { get; set; }
    public string name { get; set; }
}

public class Forecast
{
    public string dateLabel { get; set; }
    public string telop { get; set; }
    public string date { get; set; }
    public Temperature temperature { get; set; }
    public Image1 image { get; set; }
}

public class Temperature
{
    public Min min { get; set; }
    public Max max { get; set; }
}

public class Min
{
    public string celsius { get; set; }
    public string fahrenheit { get; set; }
}

public class Max
{
    public string celsius { get; set; }
    public string fahrenheit { get; set; }
}

public class Image1
{
    public int width { get; set; }
    public string url { get; set; }
    public string title { get; set; }
    public int height { get; set; }
}

WeatherHacksClass.ps1

function Main
{
    $cityCode = "130010";
    [WeatherHacks]::GetWeather($cityCode);
}

class WeatherHacks
{
    static [string]$baseUrl = "http://weather.livedoor.com/forecast/webservice/json/v1";
    static [WeatherResponse] GetWeather([string]$cityCode)
    {
        $url = "$([WeatherHacks]::baseUrl)?city=$cityCode";
        [WeatherResponse]$result = Invoke-RestMethod -Method Get -Uri $url -UseBasicParsing;
        return $result;
    }
}

class WeatherResponse
{
    [Pinpointlocation[]]$pinpointLocations;
    [string]$link;
    [Forecast[]]$forecasts;
    [Location]$location;
    [DateTime]$publicTime;
    [Copyright]$copyright;
    [string]$title;
    [Description]$description;
}

class Location
{
    [string]$city;
    [string]$area;
    [string]$prefecture;
}

class Copyright
{
    [Provider[]]$provider;
    [string]$link;
    [string]$title;
    [Image]$image;
}

class Image
{
    [int]$width;
    [string]$link;
    [string]$url;
    [string]$title;
    [int]$height;
}

class Provider
{
    [string]$link;
    [string]$name;
}

class Description
{
    [string]$text;
    [DateTime]$publicTime;
}

class Pinpointlocation
{
    [string]$link;
    [string]$name;
}

class Forecast
{
    [string]$dateLabel;
    [string]$telop;
    [string]$date;
    [Temperature]$temperature;
    [Image1]$image;
}

class Temperature
{
    [Min]$min;
    [Max]$max;
}

class Min
{
    [string]$celsius;
    [string]$fahrenheit;
}

class Max
{
    [string]$celsius;
    [string]$fahrenheit;
}

class Image1
{
    [int]$width;
    [string]$url;
    [string]$title;
    [int]$height;
}

Main

WeatherHacksFunction.ps1

function Main
{
    $cityCode = "130010";
    Get-WeatherHacksWeather -CityCode $cityCode
}
function Get-WeatherHacksWeather
{
    [OutputType([PSCustomObject])]
    [CmdletBinding()]
    param
    (
        [Parameter(Mandatory = $true)]
        [string]$cityCode
    )

    $private:baseUrl = "http://weather.livedoor.com/forecast/webservice/json/v1";
    $url = "$($baseUrl)?city=$cityCode";
    $result = Invoke-RestMethod -Method Get -Uri $url -UseBasicParsing;
    return $result;
}

Main

C# Class

PowerShell Class

PowerShell Function