Have not seen a snapshot function in the new portal either. The preview portal is still in development, so I would have an eye on it.
In the meantime you can use PowerShell as a workaround. Here are two PowerShell samples: a) how to make a snapshot and b) how to make a blob copy.
a) how to make a snapshot
https://gist.github.com/pkirch/29f5dc62fcdd640d8627
# step 1: get file
$blobFile = Get-AzureStorageBlob -Container source | Where-Object -Property Name -eq "version.txt"
# step 2: create snapshot
$cloudBlob = $blobFile.ICloudBlob
$cloudBlob.CreateSnapshot()
# step 3: get snapshots
$snapshot = Get-AzureStorageBlob -Container source | Where-Object -Property SnapshotTime
# step 4: download snapshot
$snapshot[0] | Get-AzureStorageBlobContent
b) how to make a blob copy
https://gist.github.com/pkirch/569c7880d630ddde95bb
"--> Set current storage account."
Set-AzureSubscription -SubscriptionName "My Subscription Name" -CurrentStorageAccountName "storagesource"
"--> Get blobs from containers 'source1' and 'source2' from current storage account (storagesource)."
Get-AzureStorageBlob -Container source1
Get-AzureStorageBlob -Container source2
"--> Copy BLOBs from container 'source1' into 'source2'. Each copy command shows the copied BLOBs."
"--> Copy BLOB 'Test1.txt'."
Start-AzureStorageBlobCopy -SrcBlob "Test1.txt" -SrcContainer source1 -DestContainer source2
"--> Copy BLOB 'Test2.txt'."
Start-AzureStorageBlobCopy -SrcBlob "Test2.txt" -SrcContainer source1 -DestContainer source2