Solution was very simple - httpclient didn't use any default in-memory store for cookies and I was making false assumption that it has some.
When I stored cookies on the side (and serialized them) and then - started GET request with deserialized cookies - everything worked well.
So after POST request (login):
CookieStore cookieStore = httpClient.getCookieStore();
List<Cookie> cookies = cookieStore.getCookies();
Then - serialize that list in some way. When doing GET request:
CookieStore cookieStore = new BasicCookieStore();
for(int i =0;i<cookies.length;i++) {
cookieStore.addCookie(cookies[i]);
}