In reply to MSchobitz:
Road conditions can be highly variable but you can reckon on many Highland roads not being accessible until mid-June, though that can be because the surface is in a vulnerable condition.
http://www.vegagerdin.is/media/umferd-og-faerd/Opnun_fjallvega_en_2014.pdf
Other roads can also be closed during or just after storms, but the Icelanders are resourceful and hardy, and they have a very efficient snow-ploughing system.
A lot depends on where you are heading, but there's stacks of information here:
http://www.vegagerdin.is/english
If it was me and the only thing I wanted to do was to go ice climbing, I wouldn't go to Iceland. You could be lucky but there are other venues that are more reliable and about which it's easier to obtain info. For comparison, I am heading to Iceland in March and I am planning on the basis that travel will be difficult. If it's not, then that will be a bonus, but at least I won't be disappointed.