As others have pointed out, its not so uncommon a thing. Either through local port blocking or closed relays from your ISP...
There are a few things you can do.
1) use a web client - not always optimal but remember that you outlook will sync up when you get home
2) use a 3rd pary SMTP server such as GMail...with a gmail account, you authenticate to the outgoing server so they don't consider you a spam risk. By making sure your "reply to" address is correct then messages will appear to come from your Home ISP account
3) Use a VPN - I tend to get a bit soapboxy about this point around here, but I always recomend a VPN connection when traveling. The benifits are many, not the least of which they help protect you from the prying eyes of other hotel guests. Whe a VPN connection you should be able to reach your home ISPs SMTP server just like you were at home