First, let me say Mazel Tov!
Now, Chasids for the most part are open to anyone sincerely converting into Chassidic Judaism. But, the conversion would have to be good enough for them. For example, most Orthodox would not accept a Conservative conversion, but some might. However, all Chassidic groups will not accept anything other than an Orthodox one. Still, some Orthodox conversions might not be good enough for some Chassidic sects. A modern Orthodox conversion will earn you Jewish status with most, but there are still some which will require you to go though an additional process to fully convert to their sect. But, with the exclusion of one Syrian sect that I have heard about, there shouldn't be any obstacles in your way if you truly want to convert.