Custom header to HttpClient request

var request = new HttpRequestMessage {
    RequestUri = new Uri("[your request url string]"),
    Method = HttpMethod.Post,
    Headers = {
        { "X-Version", "1" } // HERE IS HOW TO ADD HEADERS,
        { HttpRequestHeader.Authorization.ToString(), "[your authorization token]" },
        { HttpRequestHeader.ContentType.ToString(), "multipart/mixed" },//use this content type if you want to send more than one content type
    },
    Content = new MultipartContent { // Just example of request sending multipart request
        new ObjectContent<[YOUR JSON OBJECT TYPE]>(
            new [YOUR JSON OBJECT TYPE INSTANCE](...){...}, 
            new JsonMediaTypeFormatter(), 
            "application/json"), // this will add 'Content-Type' header for the first part of request
        new ByteArrayContent([BINARY DATA]) {
            Headers = { // this will add headers for the second part of request
                { "Content-Type", "application/Executable" },
                { "Content-Disposition", "form-data; filename=\"test.pdf\"" },
            },
        },
    },
};

I have found the answer to my question.

client.DefaultRequestHeaders.Add("X-Version","1");

That should add a custom header to your request

Here is an answer based on that by Anubis (which is a better approach as it doesn't modify the headers for every request) but which is more equivalent to the code in the original question:

using Newtonsoft.Json;
...

var client = new HttpClient();
var httpRequestMessage = new HttpRequestMessage
    {
        Method = HttpMethod.Post,
        RequestUri = new Uri("https://api.clickatell.com/rest/message"),
        Headers = { 
            { HttpRequestHeader.Authorization.ToString(), "Bearer xxxxxxxxxxxxxxxxxxx" },
            { HttpRequestHeader.Accept.ToString(), "application/json" },
            { "X-Version", "1" }
        },
        Content = new StringContent(JsonConvert.SerializeObject(svm))
    };

var response = client.SendAsync(httpRequestMessage).Result;